An Enhanced Adaptive Bernstein Collocation Method for Solving Systems of ODEs

Ahmad Sami Bataineh, Osman Rasit Isik, Moa’ath Oqielat and Ishak Hashim
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Ahmad Sami Bataineh: Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Al Salt 19117, Jordan
Osman Rasit Isik: Elementary Mathematics Education Program, Faculty of Education, Mugla Sitki Kocman University, Mugla 48000, Turkey
Moa’ath Oqielat: Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Al Salt 19117, Jordan
Ishak Hashim: Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, UKM, Bangi, Selangor 43600, Malaysia

Mathematics, 2021, vol. 9, issue 4, 1-15

Abstract: In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and operational matrix of differentiation with collocation method. The second method depends on tau method, the generalized Bernstein functions and operational matrix of differentiation. These methods produce a series which is obtained by non-polynomial functions set. We give the standard Bernstein polynomials to explain the generalizations for both methods. By applying the residual correction procedure to the methods, one can estimate the absolute errors for both methods and may obtain more accurate results. We apply the methods to some test examples including linear system, non-homogeneous linear system, nonlinear stiff systems, non-homogeneous nonlinear system and chaotic Genesio system. The numerical shows that the methods are efficient and work well. Increasing m yields a decrease on the errors for all methods. One can estimate the errors by using the residual correction procedure.

Keywords: nonlinearity; stiff system; ODE system; Bernstein polynomials; operational matrix of differentiation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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