A new class of time discretization schemes for the solution of nonlinear PDEs
type: Item
instance of: scholarly article
title: A new class of time discretization schemes for the solution of nonlinear PDEs
zbMATH Open document ID: 0924.65089
author: Gregory Beylkin
author: James M. Keiser
author: L. Vozovoi
published in: Journal of Computational Physics
publication date: 1999-11-02T00:00:00Z
review text: Stability of time-discretization schemes with exact treatment of the linear part (ELP schemes) for solving nonlinear partial differential equations (PDEs) is considered. ELP schemes are based on exact evaluation of the linear term. Computing and applying the exponential or other functions of operators with variable coefficients in the usual manner requires evaluating dense matrices and is highly inefficient. Using computing the exponential of strictly elliptic operators in the wavelet system of coordinates yields sparse matrices which is very effective from the numerical point of view. This fact is used for computing functions of elliptic operators with variable coefficients. In this paper this approach is developed on issues of stability and it is shown that both explicit and implicit ELP schemes have distinctly different stability properties as compared with known implicit-expilcit schemes. Examples of nonlinear diffusion equation with forcing term and Burger equation are computed using explicit ELP schemes at the end of this paper.
reviewed by: Angela Handlovičová
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1282754
zbMATH Keywords: nonlinear evolution equation
zbMATH Keywords: time discretization
zbMATH Keywords: ELP schemes
zbMATH Keywords: stability
zbMATH Keywords: numerical examples
zbMATH Keywords: method of lines
zbMATH Keywords: exact treatment of the linear part
zbMATH Keywords: wavelet system
zbMATH Keywords: sparse matrices
zbMATH Keywords: nonlinear diffusion equation
zbMATH Keywords: Burgers equation
MaRDI profile type: Publication
OpenAlex ID: W2094884329
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DOI: 10.1006/JCPH.1998.6093
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description: scientific article; zbMATH DE number 1282754