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.
Highlights
Most of the mathematical models describing real-world phenomena are often stiff ordinary differential equations (SODEs)
The results show that the proposed method is accurate and avoids the shortcoming of the classical Taylor-like explicit methods both in their component and vector forms
The results show that the generalised Taylor-like method (GTL) is stable and accurate and overcomes the overflow in computation at t = 0 by reducing the value of k from 6 to 2, without losing the convergence order and the L-stability property
Summary
Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt Institute of Engineering, Polytechnic of Porto, Rua Dr António Bernardino de Almeida, 431, 4249-015 Porto, Portugal Received: 15 October 2019; Accepted: 21 November 2019; Published: 1 December 2019
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