Computing continuous numerical solutions of matrix differential equations
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)].
scientific article; zbMATH DE number 737494