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

Authors

  • Z. A. ADEGBOYE INSTITUT DE MATHEMATIQUES ET DE SCIENCES PHYSIQUES,IMSP-UAC, DANGBO
  • Y. A. YAHAYA DEPARTMENT OF MATHEMATICAL SCIENCES, FEDERAL UNIVERSITY OF TECHNOLOGY, MINNA
  • U. I. AHMED DEPARTMENT OF MATHEMATICS AND STATISTICS, KADUNA POLYTECHNIC, KADUNA

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.

References

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Published

2020-05-08

How to Cite

ADEGBOYE, Z. A., YAHAYA, Y. A., & AHMED, U. I. (2020). DIRECT INTEGRATION OF GENERAL FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS USING FIFTH ORDER RUNGE-KUTTA METHOD. Journal of the Nigerian Mathematical Society, 39(1), 69-78. Retrieved from https://ojs.ictp.it/jnms/index.php/jnms/article/view/545

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