\(L_ 0\)-stable split linear multistep formulas for parabolic PDEs
type: Item
instance of: scholarly article
title: \(L_ 0\)-stable split linear multistep formulas for parabolic PDEs
zbMATH Open document ID: 0699.65081
DOI: 10.1016/0898-1221(90)90005-5
author: M. J. Casper
author: David A. Voss
publication date: 1990-01-01T00:00:00Z
review text: Recently \textit{J. R. Cash} [SIAM J. Numer. Anal. 21, 433-446 (1984; Zbl 0553.65084)] investigated two new classes of finite difference schemes for the numerical solution of parabolic differential equations. The main idea is to exploit the important fact that all the extrapolation methods considered by \textit{A. R. Gourlay} and \textit{J. Ll. Morris} [ibid. 17, 641- 655 (1980; Zbl 0444.65058) and IMA J. Numer. Anal. 1, 347-357 (1981; Zbl 0482.65049)] for the numerical solution of the constant coefficient, homogeneous equation \(\delta u/\delta t=Lu\), \((x,t)\in <0,1>\times <0,T>\) subject to initial condition \(u(x,0)=f(x)\), \(x\in <0,1>\) and the boundary conditions \(u(0,t)=u(1,t)=0\) for \(t\geq 0\) can be written as semi-implicit Runge-Kutta methods. On this basis new types of split linear multistep methods are applied to the numerical solution of parabolic differential equations. The formulas derived achieve up to fourth-order in time, and unlike the Crank-Nicolson method, are stable in the space \(L_ 0\).
Mathematics Subject Classification ID: 65N40
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4147450
zbMATH Keywords: \(L_ 0\)-stability
zbMATH Keywords: finite difference schemes
zbMATH Keywords: extrapolation methods
zbMATH Keywords: semi-implicit Runge-Kutta methods
zbMATH Keywords: split linear multistep methods
zbMATH Keywords: Crank- Nicolson method
describes a project that uses: MEBDF
MaRDI profile type: Publication
full work available at URL: 0898-1221(90)90005-5
OpenAlex ID: W2006378855
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cites work: Q5674335
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4147450