Nur Amirah Ahmad ¹, Norazak Senu ¹

Affiliations
1 Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, MY

Abstract

A new Two Derivative Runge-Kutta method (TDRK) based on First Same as Last (FSAL) technique for the numerical solution of first order Initial Value Problems (IVPs) is derived. We present a fourth order three stages TDRK method designed using the FSAL property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of our methods in comparison with other existing Runge-Kutta methods (RK).

Keywords

Explicit Methods, FSAL Technique, IVPs, TDRK Methods.

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Yusuf Dauda Jikantoro ¹, Fudziah Ismail ¹, Norazak Senu ¹, Mohamed Suleiman ¹

Affiliations
1 Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang Selangor, MY

Abstract

In this research, we proposed a family of improved extended Runge-Kutta-like methods which incorporate the function as well as the derivative of the function for the numerical integration of autonomous and non-autonomous ordinary differential equations. The proposed methods are more accurate than the existing methods in the literature and acquire bigger regions of stability. Numerical examples illustrating the computational accuracy are presented and the stability regions are also shown.

Keywords

Absolute Error, Absolute Stability, Extended Runge-Kutta, Ordinary Differential Equations.

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