NUMERICAL COMPARISON OF VARIOUS ORDER EXPLICIT RUNGE KUTTA METHODS WITH MATLAB ODE SOLVER
A. HASAN *
Department of Mathematics, Jazan University, Jazan, KSA.
*Author to whom correspondence should be addressed.
The purpose of this paper is, to study the numerical computation of ordinary differential equation and to show the details of implementing a few steps of Explicit RungeKutta methods, as well as how to use built-in functions available in MATLAB (2009a). In the first part, we use some Explicit RungeKutta methods to introduce the basic ideas associated with initial value problems (IVP). In the second part, we use the Runge-Kutta method and Runge-Kutta Fehlberg method presented together with the built-in MATLAB solver Ode45.The implementations that we develop in this paper are designed to build intuition and are the first step from textbook formula on ode to production software. Numerical example is given to illustrate the accuracy and robustness of these numerical methods.
Keywords: Ode, Explicit Runge Kutta methods, solver, Matlab, scientific computation, accuracy and efficiency