Open Access

ARTICLE

Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and Some Error Analysis

Radwan Abu-Gdairi¹, Shatha Hasan², Shrideh Al-Omari^3,*, Mohammad Al-Smadi^2,4, Shaher Momani^4,5

1 Department of Mathematics, Faculty of Science, Zarqa University, Zarqa, 13132, Jordan
2 Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun, 26816, Jordan
3 Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman, 11134, Jordan
4 Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, 20550, United Arab Emirates
5 Department of Mathematics, Faculty of Science, The University of Jordan, Amman, 11942, Jordan

* Corresponding Author: Shrideh Al-Omari. Email:

(This article belongs to the Special Issue: Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling)

Computer Modeling in Engineering & Sciences 2022, 130(1), 299-313. https://doi.org/10.32604/cmes.2022.017010

Received 19 April 2021; Accepted 27 July 2021; Issue published 29 November 2021

Abstract

In this paper, an efficient multi-step scheme is presented based on reproducing kernel Hilbert space (RKHS) theory for solving ordinary stiff differential systems. The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform form for a rapidly convergent series in the posed Sobolev space. Using the Gram-Schmidt orthogonality process, complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction. Consequently, by applying the standard RKHS method to each subinterval, approximate solutions that converge uniformly to the exact solutions are obtained. For this purpose, several numerical examples are tested to show proposed algorithm’s superiority, simplicity, and efficiency. The gained results indicate that the multi-step RKHS method is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.

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Citations