Stable computations by discrete mollification

The discrete mollification method is a data smoothing procedure, based on convolution, that is appropriate for the stabilization of explicit schemes for the numerical solution of partial differential equations and the regularization of ill-posed problems. This text introduces some of the main result...

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Autores:: Acosta, Carlos Daniel
Mejía, Carlos Enrique

Tipo de recurso:: Book

Fecha de publicación:: 2004

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: eng

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network_acronym_str	UNACIONAL2
network_name_str	Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv	Stable computations by discrete mollification
title	Stable computations by discrete mollification
spellingShingle	Stable computations by discrete mollification 510 - Matemáticas Ecuaciones diferenciales hiperbólicas Soluciones numéricas Diferencias finitas Leyes de conservación Matemáticas
title_short	Stable computations by discrete mollification
title_full	Stable computations by discrete mollification
title_fullStr	Stable computations by discrete mollification
title_full_unstemmed	Stable computations by discrete mollification
title_sort	Stable computations by discrete mollification
dc.creator.fl_str_mv	Acosta, Carlos Daniel Mejía, Carlos Enrique
dc.contributor.author.spa.fl_str_mv	Acosta, Carlos Daniel Mejía, Carlos Enrique
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas
topic	510 - Matemáticas Ecuaciones diferenciales hiperbólicas Soluciones numéricas Diferencias finitas Leyes de conservación Matemáticas
dc.subject.proposal.spa.fl_str_mv	Ecuaciones diferenciales hiperbólicas Soluciones numéricas Diferencias finitas Leyes de conservación Matemáticas
description	The discrete mollification method is a data smoothing procedure, based on convolution, that is appropriate for the stabilization of explicit schemes for the numerical solution of partial differential equations and the regularization of ill-posed problems. This text introduces some of the main results and recent developments in discrete mollification and discusses several important topics of current research interest. The book develops and applies numerical methods based on discrete mollification for a variety of situations arising in applied mathematics, including convection-diffusion equations, conservation laws, strongly degenerate parabolic equations and several system identification problems. For each topic there are theoretical considerations concerning stability and convergence and a generous amount of illustrative examples. The intended audience for this book includes mathematicians, physicists and engineers.
publishDate	2004
dc.date.issued.spa.fl_str_mv	2004 2014
dc.date.accessioned.spa.fl_str_mv	2020-08-21T01:49:36Z
dc.date.available.spa.fl_str_mv	2020-08-21T01:49:36Z
dc.type.spa.fl_str_mv	Libro
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/book
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/publishedVersion
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dc.type.content.spa.fl_str_mv	Text
dc.type.redcol.spa.fl_str_mv	http://purl.org/redcol/resource_type/LIB
format	http://purl.org/coar/resource_type/c_2f33
status_str	publishedVersion
dc.identifier.citation.spa.fl_str_mv	Acosta, C. D. and Bürger, R. (2012). Difference schemes stabilized by discrete mollification for degenerate parabolic equations in two space dimensions. IMA J. Numer. Anal. 32, 1509-1540. Acosta, C. D., Bürger, R., and Mejía, C. E. (2012). Monotone difference schemes stabilized by discrete mollification for strongly degenerate parabolic equations. Numerical methods for partial differential equations 28, 38-62. Acosta, C.D., Bürger, R. and Mejía C.E. (2014). A stablility and sensitivity analysis of parametric functions in a sedimentation model. DYNA 81, 22-30. Acosta, C. D. and Mejía, C. E. (2008). Stabilization of explicit methods for convection diffusion equations by discrete mollification. Comput. Math. Appl. 55, 368-380. Acosta, C. D. and Mejía, C. E. (2009). Approximate solution of hyperbolic conservation laws by discrete mollification. Applied Numerical Mathematics 59, 2256-2265. Acosta, C. D. and Mejía, C. E. (2010). A mollification based operator splitting method for convection diffusion equations. Comput. Math. Appl. 59, 1397-1408. Alexiades, V., Amienz, G., and Gremaud, P. (1996). Super-time-stepping acceleration of explicit schemes for parabolic problems. Comm. Numer. Methods Engrg. 12, 31-42. Berres, S., Bürger, R., and Garcés, R. (2010). Centrifugal settling of flocculated suspensions: a sensitivity analysis of parametric model functions. Drying Technology 28, 858-870. Berres, S., Bürger, R., Coronel, A., and Sepúlveda, M. (2005). Numerical identification of parameters for a strongly degenerate convection-diffusion problem modelling centrifugation of flocculated suspensions. Applied Numerical Mathematics 52, 311-337. Berres, S., Bürger, R., Karlsen, K. H., and Tory, E. M. (2003). Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression. SIAM J. Appl. Math. 64, 41-80. Böckmann, C., Biele, J., and Neuber, R. (1998). Analysis of multi-wavelength lidar data by inversion with mollifier method. Pure Appl. Opt. 7, 827. Bürger, R., Coronel, A., and Sepúlveda, M. (2009). Numerical solution of an inverse problem for a scalar conservation law modelling sedimentation. In J.-G. L. E. Tadmor and A. Tzavaras (Eds.), Hyperbolic Problems: Theory, Numerics and Applications. Proceedings of Symposia in Applied Mathematics, vol. 67, Part 2. American Mathematical Society. Bürger, R., Evje, S., and Karlsen, K. H. (2000). On strongly degenerate convectiondiffusion problems modeling sedimentation-consolidation processes. J. Math. Anal. Appl. 247, 517-556. Bürger, R. and Karlsen, K. H. (2001). On some upwind schemes for the phenomenological sedimentation-consolidation model. J Eng. Math. 41, 145-166. Bürger, R., Karlsen, K. H., and Towers, J. D. (2005). A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. SIAM J. Appl. Math. 65, 882-940. Bürger, R., Kozakevicius, A., and Sepúlveda, M. (2007). Multiresolution schemes for strongly degenerate parabolic equations in one space dimension. Numer Meth Partial Diff Eqns 23, 706-730. Calvetti, D., Reichel, L., and Zhang, Q. (1999). Iterative solution methods for large linear discrete ill-posed problems. Applied Comput. Control, Signals and Circuits 1, 317-374. Cecchi, M. M. and Pirozzi, M. A. (2005). High order finite difference numerical methods for time dependent convection dominated problems. Appl. Numer. Math. 55, 334-356. Cheng, Y. and Shu, C.-W. (2009). Superconvergence of local discontinuous galerkin methods for one-dimensional convection-diffusion equations. Computers and Structures 87, 630-641. Coles, C. and Murio, D. A. (2001). Simultaneous space diffusivity and source term reconstruction in 2d ihcp. Computers Math. Applic. 42, 1549-1564. Colton, D., Ewing, R., and Rundell, W. (eds.) (1990). Inverse Problems in Partial Differential Equations. Philadelphia: SIAM. Coronel, A., James, F., and Sepúlveda, M. (2003). Numerical identification of parameters for a model of sedimentation processes. Inverse Problems 19 951-972. Engquist, B. and Osher, S. (1981). One-sided difference approximations for nonlinear conservation laws. Math. Comp. 36, 321-351. Eriksson, K., Johnson, C., and Logg, A. (2003). Explicit time-stepping for stiff odes. SIAM J. Sci. Comput 25, 1142-1157. Evje, S. and Karlsen, K. H. (2000). Monotone difference approximations of bv solutions to degenerate convection-diffusion equations. SIAM J Numer. Anal. 37, 1838-1860. Faragó, I., Gnandt, B., and Havasi, A. (2008). Additive and iterative operator splitting methods and their numerical investigation. Comput. Math. Appl. 55, 2266-2279. Friedrichs, K. O. (1944). The identity of weak and strong extensions of differential operators. Trans. AMS 55, 132-151. Gilbarg, D. and Trudinger, N. S. (2001). Elliptic partial differential equations of second order. Springer. Golub, G., Heath, M., and Wahba, G. (1979, May). Generalized cross validation as a method for choosing a good ridge parameter. Technometrics 21(2), 215- 223. Hao, D. N. (1994). A mollification method for ill-posed problems. Numer. Math. 68, 469-506. Hao, D. N. (1996). A mollification method for a noncharacteristic cauchy problem for a parabolic equation. J. Math. Anal. Appl. 199, 873-909. Hao, D. N. and Reinhardt, H. J. (1997). On a sideways parabolic equation. Inverse Problems 13, 297-309. Hegland, M. and Anderssen, R. S. (1998). A mollified framework for improperly posed problems. Numer. Math. 78, 549-575. Holden, H. and Risebro, N. H. (2002). Front Tracking for Hyperbolic Conservation Laws. Springer. Karlsen, K. H., Lie, K. -A., Natvig, J. R., Nordhaug, H. F., and Dahle, H. K. (2001). Operator splitting methods for systems of convection-àrŋdiffusion equations: Nonlinear error mechanisms and correction strategies. Journal of Computational Physics 173, 636-663. Karlsen, K. H. and Risebro, N. H. (1997). An operator splitting method for nonlinear convection-diffusion equations. Numer. Math. 77, 365-382. Kelley, C. (1999). Detection and remediation of stagnation in the nelder-mead algorithm using a sufficient decrease condition. SIAM J. Optim. 10, 43-55. Lagarias, J., Reeds, J. A., Wright, M. H., and Wright, P. E. (1998). Convergence properties of the nelder-mead simplex method in low dimensions. SIAM Journal of Optimization 9, 112-147. LeVeque, R. J. (1990). Numerical Methods for Conservation Laws. Birkhauser. LeVeque, R. J. (2002). Finite Volume Methods for Hyperbolic Problems. Cambridge University Press. Louis, A. K. and Maass, P. (1990). A mollifier method for linear operator equations of the first kind. Inverse Problems 6, 427-440. Luersen, M. A. and Riche, R. L. (2004). Globalized nelder-mead method for engineering optimization. Computers and Structures 82, 2251-2260. Maass, P. and Pidcock, M. K., and Sebu, C. (2008). A mollifier method for the inverse conductivity problem. Journal of Physics: Conference Series 135, 012068. Majda, A. and Bertozzi, A. (2002). Vorticity and incompressible flow. Cambridge: Cambridge University Press. Manselli, P. and Miller, K. (1980). Calculations of the surface temperature and heat flux on one side of a wall from measurements on the opposite side. Ann. Mat. Pura Appl. 123, 161-183. Mejía, C. E. (2007). Sobre el método de molificación. Universidad Nacional de Colombia: Trabajo presentado como requisito parcial para promoción a profesor titular. Mejía, C. E., Acosta, C. D., and Saleme, K. I. (2011). Numerical identification of a nonlinear diffusion coefficient by discrete mollification. Comput. Math. Appl. 62, 2187-2199. Mejía, C. E., Murio, D. A., and S. Zhan (2001). Some applications of the mollification method. In M. Lassonde (Ed.), Approximation, Optimization and Mathematical Economics, pp. 213-222. Physica-Verlag. Mejía, C. E. and Murio, D. A. (1993). Mollified hyperbolic method for coefficient identification problems. Computers Math. Applic. 26, 1-12. Mejía, C. E. and Murio, D. A. (1995). Numerical identification of diffusivity coefficient and initial condition by discrete mollification. Comput. Math. Appl. 30, 35-50. Mejía, C. E. and Murio, D. A. (1996). Numerical solution of generalized ihcp by discrete mollification. Computers Math. Applic. 32, 33-50. Montoya, L. J., Mejía, C. E., and Toro, F. M. (2000). Estabilización de esquemas por molificación discreta. Avances en Recursos Hidráulicos 7, 102-116. Murio, D. A. (1981). The mollification method and the numerical solution of an inverse heat conduction problem. SIAM Journal on Scientific and Statistical Computing 2(1), 17-34. Murio, D. A. (1993). The Mollification Method and the Numerical Solution of III-Posed Problems. John Wiley. Murio, D. A. (2002). Mollification and space marching. In K. Woodbury (Ed.), Inverse Engineering Handbook. CRC Press. Murio, D. A. (2006). On the stable numerical evaluation of caputo fractional derivatives. Computers Math. Applic. 51, 1539-1550. Murio, D. A. (2007). Stable numerical solution of a fractional-diffusion inverse heat conduction problem. Computers Math. Applic. 53, 1492-1501. Murio, D. A. and Mejía, C. E. (2008). Source terms identification for time fractional diffusion equation. Revista Colombiana de Matemáticas 42, 25-46. Murio, D. A. and Hinestroza, D. (1989). Numerical identification of forcing terms by discrete mollification. Computers Math. Applic. 17, 1441-1447. Murio, D. A., Hinestroza, D., and Mejía, C. E. (1992). New stable numerical inversion of abel-s integral equation. Computers Math. Applic. 23, 3-11. Murio, D. A., Mejía, C. E., and Zhan, S. (1998). Discrete mollification and automatic numerical differentiation. Computers Math. Applic. 35, 1-16. Nessyahu, H. and Tadmor, E. (1990). Non-oscillatory central differencing for hyperbolic conservation laws. J. Comp. Phys. 87(2), 408-463. Ng, M. K., Chan, R. H., and Tang, W. (1999). A fast algorithm for deblurring models with neumann boundary conditions. SIAM J. Sci. Comput. 21(3), 851- 866. Price, C., Coope, I. D., and Byatt, D. (2002). A convergent variant of the neldermead algorithm. Journal of Optimization Theory and Applications 113, 5-19. Pulgarín, J. D., Acosta, C. D. and Castellanos, G. (2009). Multiscale analysis by means of discrete mollification for ecg noise reduction. DYNA 76, 185-191. Saleme, K. (2009). Identificación de coeficientes y el método de molificación. Medellín, Colombia: Master’s Thesis, Department of Mathematics, National University of Colombia. Schuster, T. and Quinto, E. T. (2005). On a regularization scheme for linear operators in distribution spaces with an application to the spherical radon transform. SIAM J. Appl. Math. 65, 1369-1387. Shu, C. W. (1998). Essentially non-oscillatory and weighted essentially nonoscillatory schemes for hyperbolic conservation laws. In A. Quarteroni (Ed.), Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lectures Notes in Mathematics, Vol 1697, pp. 325-432. Springer, Berlin. Smith, S. W. (1999). The Scientist and Engineer-s Guide to Digital Signal Processing. San Diego, California, http://www.dspguide.com: California Technical Publishing. Vogel, C. R. (2006). Computational methods for inverse problems. SIAM. Wubs, F. W. (1986). Stabilization of explicit methods for hyperbolic partial differential equations. Internat. J. Numer. Methods Fluids 6, 641-657. Yi, Z. and Murio, D. A. (2004a). Identification of source terms in 2-d ihcp. Computers Math. Applic. 47, 1517-1533. Yi, Z. and Murio, D.A. (2004b). Source term identification in 1-D IHCP. Computers Math. Applic. 47, 1921-1933. Zhan, S., Coles, C., and Murio, D. A. (2001). Automatic numerical solution of generalized 2-d ihcp by discrete mollification. Computers Math. Applic. 41, 15-38. Zhang, S. and Shu, C.-W. (2007). A new smoothness indicator for weno schemes and its effect on the convergence to steady state solutions. J. Sci. Comput. 31, 273-305. Zhao, Q. H., Urosevíc, D., Mladenovi, N., and Hansen, P. (2009). A restarted and modified simplex search for unconstrained optimization. Computers & Operations Research 36, 3263-3271.
dc.identifier.isbn.spa.fl_str_mv	9789587617542
dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/78135
identifier_str_mv	Acosta, C. D. and Bürger, R. (2012). Difference schemes stabilized by discrete mollification for degenerate parabolic equations in two space dimensions. IMA J. Numer. Anal. 32, 1509-1540. Acosta, C. D., Bürger, R., and Mejía, C. E. (2012). Monotone difference schemes stabilized by discrete mollification for strongly degenerate parabolic equations. Numerical methods for partial differential equations 28, 38-62. Acosta, C.D., Bürger, R. and Mejía C.E. (2014). A stablility and sensitivity analysis of parametric functions in a sedimentation model. DYNA 81, 22-30. Acosta, C. D. and Mejía, C. E. (2008). Stabilization of explicit methods for convection diffusion equations by discrete mollification. Comput. Math. Appl. 55, 368-380. Acosta, C. D. and Mejía, C. E. (2009). Approximate solution of hyperbolic conservation laws by discrete mollification. Applied Numerical Mathematics 59, 2256-2265. Acosta, C. D. and Mejía, C. E. (2010). A mollification based operator splitting method for convection diffusion equations. Comput. Math. Appl. 59, 1397-1408. Alexiades, V., Amienz, G., and Gremaud, P. (1996). Super-time-stepping acceleration of explicit schemes for parabolic problems. Comm. Numer. Methods Engrg. 12, 31-42. Berres, S., Bürger, R., and Garcés, R. (2010). Centrifugal settling of flocculated suspensions: a sensitivity analysis of parametric model functions. Drying Technology 28, 858-870. Berres, S., Bürger, R., Coronel, A., and Sepúlveda, M. (2005). Numerical identification of parameters for a strongly degenerate convection-diffusion problem modelling centrifugation of flocculated suspensions. Applied Numerical Mathematics 52, 311-337. Berres, S., Bürger, R., Karlsen, K. H., and Tory, E. M. (2003). Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression. SIAM J. Appl. Math. 64, 41-80. Böckmann, C., Biele, J., and Neuber, R. (1998). Analysis of multi-wavelength lidar data by inversion with mollifier method. Pure Appl. Opt. 7, 827. Bürger, R., Coronel, A., and Sepúlveda, M. (2009). Numerical solution of an inverse problem for a scalar conservation law modelling sedimentation. In J.-G. L. E. Tadmor and A. Tzavaras (Eds.), Hyperbolic Problems: Theory, Numerics and Applications. Proceedings of Symposia in Applied Mathematics, vol. 67, Part 2. American Mathematical Society. Bürger, R., Evje, S., and Karlsen, K. H. (2000). On strongly degenerate convectiondiffusion problems modeling sedimentation-consolidation processes. J. Math. Anal. Appl. 247, 517-556. Bürger, R. and Karlsen, K. H. (2001). On some upwind schemes for the phenomenological sedimentation-consolidation model. J Eng. Math. 41, 145-166. Bürger, R., Karlsen, K. H., and Towers, J. D. (2005). A model of continuous sedimentation of flocculated suspensions in clarifier-thickener units. SIAM J. Appl. Math. 65, 882-940. Bürger, R., Kozakevicius, A., and Sepúlveda, M. (2007). Multiresolution schemes for strongly degenerate parabolic equations in one space dimension. Numer Meth Partial Diff Eqns 23, 706-730. Calvetti, D., Reichel, L., and Zhang, Q. (1999). Iterative solution methods for large linear discrete ill-posed problems. Applied Comput. Control, Signals and Circuits 1, 317-374. Cecchi, M. M. and Pirozzi, M. A. (2005). High order finite difference numerical methods for time dependent convection dominated problems. Appl. Numer. Math. 55, 334-356. Cheng, Y. and Shu, C.-W. (2009). Superconvergence of local discontinuous galerkin methods for one-dimensional convection-diffusion equations. Computers and Structures 87, 630-641. Coles, C. and Murio, D. A. (2001). Simultaneous space diffusivity and source term reconstruction in 2d ihcp. Computers Math. Applic. 42, 1549-1564. Colton, D., Ewing, R., and Rundell, W. (eds.) (1990). Inverse Problems in Partial Differential Equations. Philadelphia: SIAM. Coronel, A., James, F., and Sepúlveda, M. (2003). Numerical identification of parameters for a model of sedimentation processes. Inverse Problems 19 951-972. Engquist, B. and Osher, S. (1981). One-sided difference approximations for nonlinear conservation laws. Math. Comp. 36, 321-351. Eriksson, K., Johnson, C., and Logg, A. (2003). Explicit time-stepping for stiff odes. SIAM J. Sci. Comput 25, 1142-1157. Evje, S. and Karlsen, K. H. (2000). Monotone difference approximations of bv solutions to degenerate convection-diffusion equations. SIAM J Numer. Anal. 37, 1838-1860. Faragó, I., Gnandt, B., and Havasi, A. (2008). Additive and iterative operator splitting methods and their numerical investigation. Comput. Math. Appl. 55, 2266-2279. Friedrichs, K. O. (1944). The identity of weak and strong extensions of differential operators. Trans. AMS 55, 132-151. Gilbarg, D. and Trudinger, N. S. (2001). Elliptic partial differential equations of second order. Springer. Golub, G., Heath, M., and Wahba, G. (1979, May). Generalized cross validation as a method for choosing a good ridge parameter. Technometrics 21(2), 215- 223. Hao, D. N. (1994). A mollification method for ill-posed problems. Numer. Math. 68, 469-506. Hao, D. N. (1996). A mollification method for a noncharacteristic cauchy problem for a parabolic equation. J. Math. Anal. Appl. 199, 873-909. Hao, D. N. and Reinhardt, H. J. (1997). On a sideways parabolic equation. Inverse Problems 13, 297-309. Hegland, M. and Anderssen, R. S. (1998). A mollified framework for improperly posed problems. Numer. Math. 78, 549-575. Holden, H. and Risebro, N. H. (2002). Front Tracking for Hyperbolic Conservation Laws. Springer. Karlsen, K. H., Lie, K. -A., Natvig, J. R., Nordhaug, H. F., and Dahle, H. K. (2001). Operator splitting methods for systems of convection-àrŋdiffusion equations: Nonlinear error mechanisms and correction strategies. Journal of Computational Physics 173, 636-663. Karlsen, K. H. and Risebro, N. H. (1997). An operator splitting method for nonlinear convection-diffusion equations. Numer. Math. 77, 365-382. Kelley, C. (1999). Detection and remediation of stagnation in the nelder-mead algorithm using a sufficient decrease condition. SIAM J. Optim. 10, 43-55. Lagarias, J., Reeds, J. A., Wright, M. H., and Wright, P. E. (1998). Convergence properties of the nelder-mead simplex method in low dimensions. SIAM Journal of Optimization 9, 112-147. LeVeque, R. J. (1990). Numerical Methods for Conservation Laws. Birkhauser. LeVeque, R. J. (2002). Finite Volume Methods for Hyperbolic Problems. Cambridge University Press. Louis, A. K. and Maass, P. (1990). A mollifier method for linear operator equations of the first kind. Inverse Problems 6, 427-440. Luersen, M. A. and Riche, R. L. (2004). Globalized nelder-mead method for engineering optimization. Computers and Structures 82, 2251-2260. Maass, P. and Pidcock, M. K., and Sebu, C. (2008). A mollifier method for the inverse conductivity problem. Journal of Physics: Conference Series 135, 012068. Majda, A. and Bertozzi, A. (2002). Vorticity and incompressible flow. Cambridge: Cambridge University Press. Manselli, P. and Miller, K. (1980). Calculations of the surface temperature and heat flux on one side of a wall from measurements on the opposite side. Ann. Mat. Pura Appl. 123, 161-183. Mejía, C. E. (2007). Sobre el método de molificación. Universidad Nacional de Colombia: Trabajo presentado como requisito parcial para promoción a profesor titular. Mejía, C. E., Acosta, C. D., and Saleme, K. I. (2011). Numerical identification of a nonlinear diffusion coefficient by discrete mollification. Comput. Math. Appl. 62, 2187-2199. Mejía, C. E., Murio, D. A., and S. Zhan (2001). Some applications of the mollification method. In M. Lassonde (Ed.), Approximation, Optimization and Mathematical Economics, pp. 213-222. Physica-Verlag. Mejía, C. E. and Murio, D. A. (1993). Mollified hyperbolic method for coefficient identification problems. Computers Math. Applic. 26, 1-12. Mejía, C. E. and Murio, D. A. (1995). Numerical identification of diffusivity coefficient and initial condition by discrete mollification. Comput. Math. Appl. 30, 35-50. Mejía, C. E. and Murio, D. A. (1996). Numerical solution of generalized ihcp by discrete mollification. Computers Math. Applic. 32, 33-50. Montoya, L. J., Mejía, C. E., and Toro, F. M. (2000). Estabilización de esquemas por molificación discreta. Avances en Recursos Hidráulicos 7, 102-116. Murio, D. A. (1981). The mollification method and the numerical solution of an inverse heat conduction problem. SIAM Journal on Scientific and Statistical Computing 2(1), 17-34. Murio, D. A. (1993). The Mollification Method and the Numerical Solution of III-Posed Problems. John Wiley. Murio, D. A. (2002). Mollification and space marching. In K. Woodbury (Ed.), Inverse Engineering Handbook. CRC Press. Murio, D. A. (2006). On the stable numerical evaluation of caputo fractional derivatives. Computers Math. Applic. 51, 1539-1550. Murio, D. A. (2007). Stable numerical solution of a fractional-diffusion inverse heat conduction problem. Computers Math. Applic. 53, 1492-1501. Murio, D. A. and Mejía, C. E. (2008). Source terms identification for time fractional diffusion equation. Revista Colombiana de Matemáticas 42, 25-46. Murio, D. A. and Hinestroza, D. (1989). Numerical identification of forcing terms by discrete mollification. Computers Math. Applic. 17, 1441-1447. Murio, D. A., Hinestroza, D., and Mejía, C. E. (1992). New stable numerical inversion of abel-s integral equation. Computers Math. Applic. 23, 3-11. Murio, D. A., Mejía, C. E., and Zhan, S. (1998). Discrete mollification and automatic numerical differentiation. Computers Math. Applic. 35, 1-16. Nessyahu, H. and Tadmor, E. (1990). Non-oscillatory central differencing for hyperbolic conservation laws. J. Comp. Phys. 87(2), 408-463. Ng, M. K., Chan, R. H., and Tang, W. (1999). A fast algorithm for deblurring models with neumann boundary conditions. SIAM J. Sci. Comput. 21(3), 851- 866. Price, C., Coope, I. D., and Byatt, D. (2002). A convergent variant of the neldermead algorithm. Journal of Optimization Theory and Applications 113, 5-19. Pulgarín, J. D., Acosta, C. D. and Castellanos, G. (2009). Multiscale analysis by means of discrete mollification for ecg noise reduction. DYNA 76, 185-191. Saleme, K. (2009). Identificación de coeficientes y el método de molificación. Medellín, Colombia: Master’s Thesis, Department of Mathematics, National University of Colombia. Schuster, T. and Quinto, E. T. (2005). On a regularization scheme for linear operators in distribution spaces with an application to the spherical radon transform. SIAM J. Appl. Math. 65, 1369-1387. Shu, C. W. (1998). Essentially non-oscillatory and weighted essentially nonoscillatory schemes for hyperbolic conservation laws. In A. Quarteroni (Ed.), Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lectures Notes in Mathematics, Vol 1697, pp. 325-432. Springer, Berlin. Smith, S. W. (1999). The Scientist and Engineer-s Guide to Digital Signal Processing. San Diego, California, http://www.dspguide.com: California Technical Publishing. Vogel, C. R. (2006). Computational methods for inverse problems. SIAM. Wubs, F. W. (1986). Stabilization of explicit methods for hyperbolic partial differential equations. Internat. J. Numer. Methods Fluids 6, 641-657. Yi, Z. and Murio, D. A. (2004a). Identification of source terms in 2-d ihcp. Computers Math. Applic. 47, 1517-1533. Yi, Z. and Murio, D.A. (2004b). Source term identification in 1-D IHCP. Computers Math. Applic. 47, 1921-1933. Zhan, S., Coles, C., and Murio, D. A. (2001). Automatic numerical solution of generalized 2-d ihcp by discrete mollification. Computers Math. Applic. 41, 15-38. Zhang, S. and Shu, C.-W. (2007). A new smoothness indicator for weno schemes and its effect on the convergence to steady state solutions. J. Sci. Comput. 31, 273-305. Zhao, Q. H., Urosevíc, D., Mladenovi, N., and Hansen, P. (2009). A restarted and modified simplex search for unconstrained optimization. Computers & Operations Research 36, 3263-3271. 9789587617542
url	https://repositorio.unal.edu.co/handle/unal/78135
dc.language.iso.spa.fl_str_mv	eng
language	eng
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spelling	Atribución-NoComercial-SinDerivadas 4.0 InternacionalDerechos reservados - Universidad Nacional de ColombiaAcceso abiertohttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Acosta, Carlos Daniel96e95e3b-f5f9-4307-93fa-9efcb10c532dMejía, Carlos Enriqueb92a35f8-aeb2-4f74-9eaf-10ac9927a42f2020-08-21T01:49:36Z2020-08-21T01:49:36Z20042014Acosta, C. D. and Bürger, R. (2012). Difference schemes stabilized by discrete mollification for degenerate parabolic equations in two space dimensions. IMA J. Numer. Anal. 32, 1509-1540. Acosta, C. D., Bürger, R., and Mejía, C. E. (2012). Monotone difference schemes stabilized by discrete mollification for strongly degenerate parabolic equations. Numerical methods for partial differential equations 28, 38-62. Acosta, C.D., Bürger, R. and Mejía C.E. (2014). A stablility and sensitivity analysis of parametric functions in a sedimentation model. DYNA 81, 22-30. Acosta, C. D. and Mejía, C. E. (2008). Stabilization of explicit methods for convection diffusion equations by discrete mollification. Comput. Math. Appl. 55, 368-380. Acosta, C. D. and Mejía, C. E. (2009). Approximate solution of hyperbolic conservation laws by discrete mollification. Applied Numerical Mathematics 59, 2256-2265. Acosta, C. D. and Mejía, C. E. (2010). A mollification based operator splitting method for convection diffusion equations. Comput. Math. Appl. 59, 1397-1408. Alexiades, V., Amienz, G., and Gremaud, P. (1996). Super-time-stepping acceleration of explicit schemes for parabolic problems. Comm. Numer. Methods Engrg. 12, 31-42. Berres, S., Bürger, R., and Garcés, R. (2010). Centrifugal settling of flocculated suspensions: a sensitivity analysis of parametric model functions. Drying Technology 28, 858-870. Berres, S., Bürger, R., Coronel, A., and Sepúlveda, M. (2005). 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Computers & Operations Research 36, 3263-3271.9789587617542https://repositorio.unal.edu.co/handle/unal/78135The discrete mollification method is a data smoothing procedure, based on convolution, that is appropriate for the stabilization of explicit schemes for the numerical solution of partial differential equations and the regularization of ill-posed problems. This text introduces some of the main results and recent developments in discrete mollification and discusses several important topics of current research interest. The book develops and applies numerical methods based on discrete mollification for a variety of situations arising in applied mathematics, including convection-diffusion equations, conservation laws, strongly degenerate parabolic equations and several system identification problems. For each topic there are theoretical considerations concerning stability and convergence and a generous amount of illustrative examples. The intended audience for this book includes mathematicians, physicists and engineers."Para leer esta publicación se requiere un programa de lectura de libros digitales, como el Adobe Digital Editions® https://www.adobe.com/la/solutions/ebook/digital-editions/download.html"110engUNIVERSIDAD NACIONAL DE COLOMBIA510 - MatemáticasEcuaciones diferenciales hiperbólicasSoluciones numéricasDiferencias finitasLeyes de conservaciónMatemáticasStable computations by discrete mollificationLibroinfo:eu-repo/semantics/bookinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2f33http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/LIBEvaluada por paresORIGINAL9789587617542.pdf9789587617542.pdfapplication/pdf1200979https://repositorio.unal.edu.co/bitstream/unal/78135/1/9789587617542.pdf064d925dad768203bfd7862716ad4cbaMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-83895https://repositorio.unal.edu.co/bitstream/unal/78135/2/license.txte2f63a891b6ceb28c3078128251851bfMD52CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.unal.edu.co/bitstream/unal/78135/3/license_rdf217700a34da79ed616c2feb68d4c5e06MD53THUMBNAIL9789587617542.pdf.jpg9789587617542.pdf.jpgGenerated Thumbnailimage/jpeg4202https://repositorio.unal.edu.co/bitstream/unal/78135/4/9789587617542.pdf.jpg0a62e559cc419dd673616e0ef1dfc247MD54unal/78135oai:repositorio.unal.edu.co:unal/781352024-07-06 23:51:54.769Repositorio Institucional Universidad Nacional de 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GVyZWNob3MgZGUgYXV0b3IgcXVlIGNvbmxsZXZlIGxhIGRpc3RyaWJ1Y2nDs24gZGUgZXN0b3MgYXJjaGl2b3MgeSBtZXRhZGF0b3MuCkFsIGhhY2VyIGNsaWMgZW4gZWwgc2lndWllbnRlIGJvdMOzbiwgdXN0ZWQgaW5kaWNhIHF1ZSBlc3TDoSBkZSBhY3VlcmRvIGNvbiBlc3RvcyB0w6lybWlub3MuCg==

Stable computations by discrete mollification

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