Computing continuous numerical solutions of matrix differential equations
type: Item
instance of: scholarly article
title: Computing continuous numerical solutions of matrix differential equations
zbMATH Open document ID: 0819.65107
DOI: 10.1016/0898-1221(94)00240-L
publication date: 1995-09-06T00:00:00Z
review text: This paper is concerned with the numerical solution of initial value problems for matrix differential equations of type \(X'(t) = A(t) X(t) + X(t) B(t) + L(t)\), where the square coefficient matrices \(A(t)\), \(B(t)\) and \(L(t)\) are sufficiently smooth. The numerical solution proposed by the authors is an interpolatory \(B\)- spline of the exact solution on an equidistributed set of knots in the integration interval. By using standard techniques of difference equations the uniform convergence (in the sense of \(\varepsilon\)- approximate solutions) of the numerical solution to the exact solution in a suitable subset of the integration interval is proved. Finally, to point out that some statements given by the authors in the introduction of the paper on the maximal interval of existence of solutions of linear systems of differential equations with continuous coefficients, appear to be in clear contradiction with the standard theory on this subject [e.g. \textit{Ph. Hartmann}, Ordinary differential equations (1964; Zbl 0125.321)].
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 737494
zbMATH Keywords: interpolatory \(B\)-spline
zbMATH Keywords: matrix differential equations
zbMATH Keywords: difference equations
zbMATH Keywords: uniform convergence
zbMATH Keywords: linear systems
author: L. Jódar
author: E. Ponsoda
reviewed by: Manuel Calvo
MaRDI profile type: Publication
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full work available at URL: 0898-1221(94)00240-l
OpenAlex ID: W2080025785
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 737494