On conditions for the absolute stability of one difference scheme for some multidimensional differential-algebraic systems

The paper considers an initial-boundary value problem for a linear multidimensional differential-algebraic system of equations of the first order with variable matrix coefficients of a special form. For its numerical solution, the spline-collocation method was used. This method, in contrast to the splitting methods, allows one to take into account the structural features of all matrix coefficients of the system in aggregate and has a high accuracy, which coincides with the order of the multidimensional approximating spline. The paper contains a multidimensional spline-collocation difference scheme. A theorem on the stability of the difference scheme under certain conditions on the matrix coefficients of the system is proved. In conclusion, the results of numerical calculations for the test example are given.