The G-Euler process for nonlinear autonomous systems

Abstract

The G-Euler process is an improved version of the Lawson method (SIAM J Numer Anal 4:372-380, 1967). This paper is concerned with the behaviors of true solutions and numerical solutions, and shows that the G-Euler process preserves the behaviors of true solutions with a suitable choice of stepsize. The rate of coincidence of behaviors is introduced instead of the relative error. By using the minimum rate of coincidence of behaviors, we also show that the numerical solutions computed by the G-Euler process follow the true solutions of nonlinear autonomous systems to the last.