1Department of Mathematics, Ekiti State University, Ado Ekiti, Nigeria.
2 Department of Mathematics and Statistics, The Federal Polytechnic, Ado Ekiti, Nigeria.
Research Article
World Journal of Advanced Research and Reviews, 2021, 09(01), 239-249
Article DOI: 10.30574/wjarr.2021.9.1.0012
Received on 10 January 2021; revised on 18 January 2021; accepted on 20 January 2021
This paper focuses on the derivation, analysis and implementation of a hybrid method by optimizing the order of the method by introduction of six-hybrid points for direct solution of fifth order ordinary differential equations of initial value problems (IVPs). Power series was used as the basis function for the solution of the IVP. The basis function was interpolated at some selected hybrid points whereas the fifth derivative of the approximate solution was collocated at all the interval of integration of the method to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was tested with two linear test problems to confirm its accuracy and usability. The comparison of the results with some existing methods shows the superiority of the accuracy of the method.
AMS Subject Classification: 65L05, 65L06, 65L10, 65L12
Hybrid Method; Fifth Order ODEs; Initial Conditions; Linear Fifth Order Problems
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Roseline Bosede Ogunrinde, Ololade Funmilayo Fayose and Taiwo Stephen Fayose. Optimization of one-step hybrid method for direct solution of fifth order ordinary differential equations of initial value problems. World Journal of Advanced Research and Reviews, 2021, 9(1), 239-249. Article DOI: https://doi.org/10.30574/wjarr.2021.9.1.0012