On the Stability of Spline Collocation Difference Scheme for Linear Multidimensional Differential-Algebraic Systems

An initial-boundary value problem is considered for a linear multidimensional differential-algebraic system of first-order equations with variable matrix coefficients of a special form. A spline collocation method is used to solve it numerically. Unlike splitting methods, this method allows taking into account the structural features of all matrix coefficients of the system in total and has a high accuracy, which coincides with the order of the multidimensional approximating spline. A multidimensional spline collocation difference scheme is presented. A theorem on the stability of the difference scheme under certain conditions on the matrix coefficients of the system is proved. Finally, the results of numerical calculations for the test example are given.