Error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations
type: Item
instance of: scholarly article
title: Error estimates for single step fully discrete approximations for nonlinear second order hyperbolic equations
zbMATH Open document ID: 0654.65074
DOI: 10.1016/0898-1221(88)90279-9
publication date: 1988-01-01T00:00:00Z
review text: In an earlier paper [ibid. 12A, 581-604 (1986; Zbl 0596.65079)] the author considered the problem: \[ (1)\quad u_{tt}=\sum^{N}_{j,k=1}\partial /\partial x_ j[a_{j_ k}(x,t,u)\partial u/\partial x_ k]-a_ 0(x,t,u)u+f(x,t,u,u_ t,\nabla u) \] u\(=0\) in \(\Omega\) \(\times [0,\tau]\) \(u(0)=u^ 0\), \(u_ t(0)=u^ 0_ t\) in \(\Omega\), where \(\Omega\) is bounded in \(R^ N\), \(1\leq N\leq 3\) when f is independent of \(u_ t\) and u. The aim of the present paper is to give single step methods for numerically solving the more general case (1).
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 4068210
zbMATH Keywords: error estimates
zbMATH Keywords: rate of convergence
zbMATH Keywords: single step methods
author: Laurence A. Bales
MaRDI profile type: Publication
full work available at URL: 0898-1221(88)90279-9
OpenAlex ID: W1977415733
cites work: Higher-order single-step fully discrete approximations for nonlinear second-order hyperbolic equations
cites work: Higher Order Single Step Fully Discrete Approximations for Second Order Hyperbolic Equations with Time Dependent Coefficients
cites work: Efficient Higher Order Single Step Methods for Parabolic Problems: Part I
cites work: Semidiscrete and single step fully discrete approximations for second order hyperbolic equations with time-dependent coefficients
cites work: Galerkin/Runge–Kutta Discretizations for Semilinear Parabolic Equations
cites work: Galerkin finite element methods for parabolic problems
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4068210