An optimized single-step method for integrating Cauchy problems

Abstract

This work involves development of an optimum third order single-step explicit method for Cauchy problems. The proposed method is analyzed for consistency, stability, local and global error bounds, and convergence. Further, numerical investigation is carried out to assess effectiveness of the method in comparison to existing numerical schemes, including Modified Improved Modified Euler (MIME) method, Third order Euler method (TOEM) and classical Runge-Kutta method of order three (RK3). The testing factors are error and CPU time which have been computed using Matlab R2014b. It is observed that the proposed method possesses minimum error bounds; and is also favourable in terms of both accuracy and computational cost.