Semi-analytic time-marching algorithms for semilinear parabolic equations
type: Item
instance of: scholarly article
title: Semi-analytic time-marching algorithms for semilinear parabolic equations
zbMATH Open document ID: 0821.65063
DOI: 10.1007/BF01935022
author: Vladimir Karlin
author: V. Maz'ya
published in: BIT
publication date: 1995-09-27T00:00:00Z
review text: New time marching algorithms for the numerical solution of semilinear parabolic equations are described. They are based on the approximation method proposed by the first author (based upon the use of approximate partition of unity). The algorithms developed in this paper give the time step approximation in the form of an analytic function, which enables one to differentiate the approximate solution with respect to \(x\) explicitly. The algorithms are flexible in the choice of the basis functions and they can be generalized to the multidimensional case easier than spline approximations and other finite element procedures. An important advantage is the possibility to obtain explicit formulae for values of various integral and pseudodifferential operators of mathematical physics applied to the basis functions. The algorithms are stable under mild restrictions to the time step, which come from the nonlinear part of the equation.
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 716132
zbMATH Keywords: time marching algorithms
zbMATH Keywords: semilinear parabolic equations
zbMATH Keywords: partition of unity
zbMATH Keywords: finite element
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: basis functions
reviewed by: Margit Lenard
MaRDI profile type: Publication
cites work: A table of solutions of the one-dimensional Burgers equation
cites work: Q3675490
cites work: Q5536978
full work available at URL: https://doi.org/10.1007/bf01935022
OpenAlex ID: W1985955326
description: scientific article; zbMATH DE number 716132