Applied mathematics

Direct method for solving systems of second order ordinary differential equations

I. V. Olemskoy, A. S. Eremin, A. V. Matrosov

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: In the paper a direct solver for systems of structurally partitioned second order differential equations is proposed. a general scheme of the method algorithmically oriented towards the particular structure of the system is presented. With the last stage reuse (also known as FSAL approach) an embedded pair of sixth and fourth order methods with just six stages is constructed, which provides an easy step-size control. Numerical comparison is made with the well-known Dormand — Prince method 5(4)7F having the same computation cost, showing the advantage of the proposed method.

Keywords: Runge — Kutta methods, second order equations, structurall partitioned system, sixth order.

UDC: 519.62, 519.622

MSC: 65L05, 65L06

Received: May 16, 2024
Accepted: June 25, 2024

DOI: 10.21638/spbu10.2024.302