Numerical Adaptive Method of Solving the Systems of Linear Differential Equations with Variable Coefficients

A high-precision numerical adaptive method of integration of the systems of linear differential equations with time-varying coefficients is presented in the paper. The adaptability of the method lies in the fact that at each step of the integration, threre is the refinement of the result which is accomplished by adding to it a certain number of refinement terms from a Taylor series for the searched functions. The number of these terms, according to the curvature, is different, which determines the adaptability of the method. Some examples were provided.