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Asian Journal of Applied Sciences
Year: 2014  |  Volume: 7  |  Issue: 3  |  Page No.: 102 - 116

A Third-Order Direct Integrators of Runge-Kutta Type for Special Third-Order Ordinary and Delay Differential Equations

Mohammed S. Mechee, F. Ismail, Z. Siri and N. Senu    

Abstract: A two sets of test problems are tested upon, the first set consists of problems on ordinary differential equations and the second set consists of problems on delay differential equations. The problems are solved using the new RKD method and numerical comparisons are made when the same problems are reduced to a first order system of ODEs and first order system of DDEs and solved using the existing Runge-Kutta methods of order three and four. The RKD method is adapted to solve delay differential equations (DDEs). Stability polynomial of the method for linear special third order DDEs is given. The numerical results have clearly shown the advantage and the efficiency of the new method in terms of accuracy and computational time.

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