A modified group-preserving scheme for solving the initial value problems of stiff ordinary differential equations

Abstract

The group-preserving (GP) scheme, proposed by Liu [Internat. J. Non-linear Mech., 2001], which preserves the cone structure in the Minkowski space, has been developed by employing the Cayley map to form a Lie group transformation providing an explicit time integrator for the general dynamical systems. In this paper, a modification GP scheme is proposed by considering the translation of the state variables to resolve the difficulties of small time step problem in solving the initial value problem with stiffness. Several numerical examples are examined and compared with the exact solutions. It shows that the modified GP scheme works very well, and the merits of the computational efficiency and accuracy of the method can be confirmed.