Malaysian Journal of Mathematical Sciences, September 2020, Vol. 14, No. 3
Higher Order Three Derivative Runge-Kutta Method with Phase-Fitting and Amplification-Fitting Technique for Periodic IVPs
Ahmad, N. A., Senu, N., Ibrahim, Z. B., Othman, M., and Ismail, Z.
Corresponding Email: nuramirah_ahmad@yahoo.com
Received date: 28 April 2020
Accepted date: 28 August 2020
Abstract:
Two phase-fitted and amplification-fitted three derivative Runge-Kutta method (PFAFThDRK) for the numerical solution of first-order initial
value problems (IVPs) of higher algebraic order with oscillatory solutions are constructed. Using the phase-fitted and amplification-fitted property, a sixth-order three-stage and seventh-order three-stage three derivative Runge-Kutta (ThDRK) method are proposed. Using the same property of some existing Runge-Kutta methods (RK), the accuracy and efficiency of the methods constructed are compared by the means of numerical investigations.
Keywords: Diagonally Implicit methods, IVPs, ODEs, ThDRK methods, Phase-Fitted and Amplification-Fitted
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