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

Essam R. El-Zahar, José Tenreiro Machado and Abdelhalim Ebaid
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Essam R. El-Zahar: Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
José Tenreiro Machado: Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal
Abdelhalim Ebaid: Department of Mathematics, Faculty of Sciences, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia

Mathematics, 2019, vol. 7, issue 12, 1-18

Abstract: 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.

Keywords: ordinary differential equations; nonlinear high order methods; L-stability; Taylor-like explicit methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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