One-step exponential-rational methods for the numerical solution of first order initial value problems

Abstract

In this study, a new class of exponential-rational methods (ERMs) for the numerical solution of first order initial value problems has been developed. Developments of third order and fourth order ERMs, as well as their corresponding local truncation error have been presented. Each ERM was found to be consistent with the differential equation and L-stable. Numerical experiments showed that the third order and fourth order ERMs generates more accurate numerical results compared with the existing rational methods in solving first order initial value problems.