Article: A new family of L-stable block methods with relative measure of stability Journal: International Journal of Applied Nonlinear Science (IJANS) 2022 Vol.3 No.3 pp.197 - 222 Abstract: There are several nonlinear and stiff mathematical models in fields of science and engineering that have always remained a challenge for numerical analysts and applied mathematicians. Various numerical methods are proposed to deal with stiff models; however, it requires the model to have strong stability characteristics to handle the stiffness in the model. This paper develops a new family of L-stable block methods with a relative measure of stability for the solution of stiff differential equations with different characteristics. First, the theoretical properties of the proposed block method in terms of local truncation errors, absolute stability, consistency, convergence, and order stars have been analysed and investigated. Then, seven illustrative stiff differential models have been solved to measure the proposed method's performance, suitability, effectiveness, and efficiency. Finally, the error distributions and the precision factors are computed in the comparison of several existing methods having similar properties as that of the proposed L-stable block method. Inderscience Publishers - linking academia, business and industry through research

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Title: A new family of L-stable block methods with relative measure of stability

Authors: Sania Qureshi; Amanullah Soomro; Fadugba Sunday Emmanuel; Evren Hincal

Addresses: Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro – 76062, Pakistan; Department of Mathematics, Near East University, TRNC, Mersin 10, Turkey ' Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro – 76062, Pakistan ' Department of Mathematics, Faculty of Science, Ekiti State University, Ado Ekiti, 360001, Nigeria ' Department of Mathematics, Near East University, TRNC, Mersin 10, Turkey

Abstract: There are several nonlinear and stiff mathematical models in fields of science and engineering that have always remained a challenge for numerical analysts and applied mathematicians. Various numerical methods are proposed to deal with stiff models; however, it requires the model to have strong stability characteristics to handle the stiffness in the model. This paper develops a new family of L-stable block methods with a relative measure of stability for the solution of stiff differential equations with different characteristics. First, the theoretical properties of the proposed block method in terms of local truncation errors, absolute stability, consistency, convergence, and order stars have been analysed and investigated. Then, seven illustrative stiff differential models have been solved to measure the proposed method's performance, suitability, effectiveness, and efficiency. Finally, the error distributions and the precision factors are computed in the comparison of several existing methods having similar properties as that of the proposed L-stable block method.

Keywords: stiff systems; A-stability; local error; order stars; implicit stiff solver; efficiency curves.

DOI: 10.1504/IJANS.2022.125306

International Journal of Applied Nonlinear Science, 2022 Vol.3 No.3, pp.197 - 222

Received: 20 Jan 2022
Accepted: 21 Apr 2022
Published online: 06 Sep 2022 *

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Title: A new family of L-stable block methods with relative measure of stability

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