Solution of differential equations with nonseparated multipoint and integral conditions

We propose a numerical method for solving systems of linear nonautonomous ordinary differential equations with nonseparated multipoint and integral conditions. The method is based on the operation of the convolution of the integral conditions into local ones, which allows us to reduce the solution of the original problem to the solution of a Cauchy problem for ordinary differential equations and for a system of algebraic linear equations. We prove the stability of the computational schemes. Many numerical experiments on specially constructed test problems with the use of the formulas and schemes for numerical solution are proposed in the article. The experimental results showed a sufficiently high efficiency of this approach.