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.
