DIRECT INTEGRATION OF GENERAL FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS USING FIFTH ORDER RUNGE-KUTTA METHOD

Z. A. ADEGBOYE, Y. A. YAHAYA, U. I. AHMED

Abstract


In this work, the fifth-order Runge-Kutta method for the solution of first order Ordinary Differential Equations (ODEs) was modified for direct integration of general fourthorder ODEs via the idea as those invented by Nystr¨om. The theory of Nystr¨om was adopted in the derivation of the method. The method has an explicit structure for efficient implementation,
self-starting produces simultaneously approximation of the solution of special and general fourth-order ODEs. The proposed method is direct, does not involve the reduction of higher order ODEs to system of first-order ODEs as in most recent related articles, convergence analysis of the method was presented, was tested with Numerical experiment to illustrate its efficiency, could be extended to solve higher-order differential equations, simple to implement and the approximate results are in good agreement with other methods mentioned in literature.

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