Volume 5, Issue 4, December 2019, Page: 97-103
Analysis of the Properties of a Third Order Convergence Numerical Method Derived via the Transcendental Function of Exponential Form
Sunday Emmanuel Fadugba, Department of Mathematics, Faculty of Science, Ekiti State University, Ado Ekiti, Nigeria
Jethro Olorunfemi Idowu, Department of Mathematics, Faculty of Science, Ekiti State University, Ado Ekiti, Nigeria
Received: Sep. 14, 2019;       Accepted: Oct. 18, 2019;       Published: Nov. 4, 2019
DOI: 10.11648/j.ijamtp.20190504.11      View  22      Downloads  12
Abstract
This paper proposes a new numerical method for the solution of the Initial Value Problems (IVPs) of first order ordinary differential equations. The new scheme has been derived via the transcendental function of exponential type. The analysis of the properties of the method such as local truncation error, order of accuracy, consistency, stability and convergence were investigated. Two illustrative examples/test problems were solved successfully to test the accuracy, performance and suitability of the method in terms of the absolute relative errors computed at the final nodal point of the associated integration interval via MATLAB codes. It is observed that the method is found to be of third order convergence, consistent and stable. The numerical results obtained via the method agree with the exact solution. Moreover, it is also observed that the method is an improvement on Fadugba-Falodun scheme. Hence, the proposed numerical method is a good approach for solving the IVPs of various nature and characteristics in diverse areas of Ordinary Differential Equations (ODEs).
Keywords
Accuracy, Consistency, Convergence, Initial Value Problem, Local Truncation Error, Order of Accuracy, Region of Stability, Stability
To cite this article
Sunday Emmanuel Fadugba, Jethro Olorunfemi Idowu, Analysis of the Properties of a Third Order Convergence Numerical Method Derived via the Transcendental Function of Exponential Form, International Journal of Applied Mathematics and Theoretical Physics. Special Issue: Computational Mathematics. Vol. 5, No. 4, 2019, pp. 97-103. doi: 10.11648/j.ijamtp.20190504.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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