TO DEVELOP EFFICIENT SCHEME FOR SOLVING INITIAL VALUE PROBLEM IN ORDINARY DIFFERENTIAL EQUATION

Abstract

In this paper, a new scheme of Runge-Kutta (RK) type has been developed while evaluating two slope functions per step and maintaining the third order accuracy of the scheme. Local truncation error is obtained with the help of principal term which is obtained via multi variable Taylor series. It has been shown that the convergence order of the scheme is three and its stability polynomial is also derived. Some numerical examples are taken in order to compare the developed scheme with other existing schemes. It is observed that the developed scheme is better than other selected existing schemes and this comparison has been performed on the basis of slope evaluations per integration step, error analysis and computer time consumed by the scheme under consideration.

KEY WORDS: Initial value problems, Runge-Kutta Scheme, Autonomous and non-autonomous differential equations, Zero stability.

DOI: 10.7176/MTM/9-8-06

Publication date: August 31st 2019