A matrix approach to the analytic-numerical solution of mixed partial differential systems
type: Item
instance of: scholarly article
title: A matrix approach to the analytic-numerical solution of mixed partial differential systems
zbMATH Open document ID: 0839.65105
DOI: 10.1016/0898-1221(95)00071-6
publication date: 1996-06-16T00:00:00Z
review text: The paper deals with systems of linear partial differential equations of the form \[ u_t(x, t)- Au_{xx}(x, t)- Bu(x, t)= G(x, t),\quad 0< x< p,\;t> 0,\tag{1} \] where \(u= (u_1,\dots, u_m)\) is an unknown vector-function and \(A\), \(B\) are constant \(m\times m\) complex matrices. It is supposed that every eigenvalue of \({1\over 2} (A+ A^H)\) is positive (\(A^H\) denotes the conjugate transpose of \(A\)). Assuming initial and boundary conditions (2) \(u(x, 0)= F(x)\), \(u(0, t)= u(p, t)= 0\), the authors seek the solution of (1), (2) in the form of a Fourier series with respect to \(x\), whose coefficients depend on \(t\). An approximate solution is obtained by truncating this series and by suitable approximation of its coefficients. The estimate of the error is proved.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 825386
zbMATH Keywords: analytic-numerical solution
zbMATH Keywords: mixed partial differential systems
zbMATH Keywords: Schur decomposition
zbMATH Keywords: matrix norms
zbMATH Keywords: matrix functions
zbMATH Keywords: truncated Fourier series
zbMATH Keywords: spectral method
author: Enrique Navarro
author: E. Ponsoda
author: L. Jódar
reviewed by: Hanna Marcinkowska
MaRDI profile type: Publication
full work available at URL: 0898-1221(95)00071-6
OpenAlex ID: W2029065770
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 825386