A New Two Derivative FSAL Runge-Kutta Method of Order Five in Four Stages

Abstract

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

Keywords

• Explicit methods, FSAL property, Initial value problems, Two Derivative Runge-Kutta method