N-Step n + 2th order stable method for linear ordinary differential equations

Abstract

The families of the n-step methods of order n + 2 for systems of linear differential equations of the 1st order are built for even n≥4. The stability domains of the methods are found. A comparison with the Runge-Kutta 4th order method and the Dorman-Prince 8th order method was made. Numerical experiment on the model examples showed that the computation time for solving the problem can be reduced by hundreds of times for the mean-square error about 10−13–10−14 that is an important factor in the resolving laborious numerical problems in mechanics. Also carried out a comparison with the Magnus method, specialized for linear differential equations. Areas in which each of the methods has its advantages to be determined.