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Open AccessArticle

A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations

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Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
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Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt
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Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
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Department of Mathematics, Faculty of Sciences, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1154; https://doi.org/10.3390/math7121154
Received: 15 October 2019 / Revised: 15 November 2019 / Accepted: 21 November 2019 / Published: 1 December 2019
(This article belongs to the Special Issue Nonlinear Dynamics)
A new generalised Taylor-like explicit method for stiff ordinary differential equations (ODEs) is proposed. The algorithm is presented in its component and vector forms. The error and stability analysis of the method are developed showing that it has an arbitrary high order of convergence and the L-stability property. Moreover, it is verified that several integration schemes are special cases of the new general form. The method is applied on stiff problems and the numerical solutions are compared with those of the classical Taylor-like integration schemes. The results show that the proposed method is accurate and overcomes the shortcoming of the classical Taylor-like schemes in their component and vector forms. View Full-Text
Keywords: ordinary differential equations; nonlinear high order methods; L-stability; Taylor-like explicit methods ordinary differential equations; nonlinear high order methods; L-stability; Taylor-like explicit methods
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MDPI and ACS Style

El-Zahar, E.R.; Tenreiro Machado, J.; Ebaid, A. A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations. Mathematics 2019, 7, 1154.

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