A HYBRID NUMERICAL METHOD WITH GREATER EFFICIENCY FOR SOLVING INITIAL VALUE PROBLEMS

Abstract

The main focus of this paper is to develop hybrid numerical method with greater efficiency for getting the solution of initial value problems (IVPs) in ordinary differential equations (ODEs) by merging the slopes used in Modified Euler’s method (MEM), Improved Euler’s method and a 2^nd stage 2^nd order contra harmonic mean method. Developed method has tested and analyzed for the stability, consistency and accuracy and observed that the developed method is more stable, consistent and accurate as compared to modified Euler’s method (MEM), Improved Euler’s method(IEM), modified improved modified Euler’s method (MIME) and a 2nd stage 2^nd order contra harmonic mean method (C₀M).

Keywords: A hybrid numerical method, Ordinary differential equations, Initial value problems, Stability and consistency