DEVELOPMENT OF ACCELERATED THIRD ORDER RUNGE KUTTA METHOD FOR NON-AUTONOMOUS ORDINARY DIFFERENTIAL EQUATION

Abstract

In this article, we derive well-organized third order numerical technique for IVP of ODE’s including partial derivative which has enhanced its competency regarding truncation error. This new accelerated proposed scheme is used to evaluate numerically ODE’s with initial condition. For this, several numerical examples are tested. Last Absolute Error, Maximum Absolute Error and CPU Time has calculated. Convergence of an accelerated proposed method is diagnosed by testing several problems and its consequence verified with available methods. Numerical results are given for proposed scheme to illustrate the accuracy and efficiency. The comparisons of the proposed and existing schemes having same order of local accuracy are discussed. Based on the results, the proposed scheme gives the better result than few same order methods. MATLAB 2023a is preferred for numerically and graphically analysis of methods