A proposed sixth order inverse polynomial method for the solution of non-linear physical models

Volume 32, Issue 2, pp 94--108 http://dx.doi.org/10.22436/jmcs.032.02.01

Publication Date: August 01, 2023 Submission Date: August 22, 2022 Revision Date: June 11, 2023 Accteptance Date: June 21, 2023

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Authors

S. E. Fadugba - Department of Physical Sciences, Mathematics Programme, Landmark University, Omu-Aran, Nigeria. - Department of Mathematics, Ekiti State University, Ado Ekiti, 360001, Nigeria. - Landmark University SDG 4: Quality Education Research Group, Omu-Aran, Nigeria. I. Ibrahim - Department of Mathematics, Federal University, Dutse, Nigeria. O. Adeyeye - School of Quantitative Sciences , Universiti Utara Malaysia (UUM), Kedah, Malaysia. A. A. Adeniji - Department of Mathematics, Tshwane University of Technology, Pretoria, South Africa. M. C. Kekana - Department of Mathematics, Tshwane University of Technology, Pretoria, South Africa. J. T. Okunlola - Department of Mathematical and Physical Sciences, Afe Babalola University, Ado Ekiti, Nigeria.

Abstract

There are several nonlinear physical models emanated from science and technology that have always remained a challenge for numerical analysts and applied mathematicians. Various one-step numerical methods were developed to deal with these models, however, it requires the developed method to have consistency, stability, zero stability and convergence characteristics to handle the non-linearity in the model. This paper proposes a new sixth order inverse polynomial method (SOIPM) with a relative measure of stability for the solution of non-linear physical models with different flavors. Firstly, the properties of SOIPM are analyzed and investigated. Moreover, three illustrative non-linear physical models have been solved to measure the accuracy, computational performance, suitability and effectiveness of SOIPM. Furthermore, the results generated via SOIPM are compared with the existing method of the celebrated Runge-Kutta of order four (RK4) in the context of the exact value (EV). Finally, the absolute errors (ABEs) and final absolute errors (FABEs) incurred by SOIPM are computed and compared with that of RK4.

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Keywords

• Consistency
• convergence
• initial value problem
• inverse polynomial method
• linear stability
• order of accuracy
• rational interpolating polynomial
• zero stability

MSC

•  34A12
•  65L05
•  65L20
•  65L70

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