Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value Problems

Richard Olatokunbo Akinola, Ali Shokri, Shao-Wen Yao () and Stephen Yakubu Kutchin
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Richard Olatokunbo Akinola: Department of Mathematics, Faculty of Natural Sciences, University of Jos, Jos 930105, Nigeria
Ali Shokri: Department of Science, Faculty of Science, University of Maragheh, Maragheh 83111-55181, Iran
Shao-Wen Yao: School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
Stephen Yakubu Kutchin: Department of Mathematics, Faculty of Natural Sciences, University of Jos, Jos 930105, Nigeria

Mathematics, 2022, vol. 10, issue 16, 1-19

Abstract: When finding numerical solutions to stiff and nonstiff initial value problems using linear multistep methods, ill-conditioned systems are often encountered. In this paper, we demonstrate how this ill-conditioning can be circumvented without iterative refinement or preconditioning, by carefully choosing the grid point used in deriving the discrete scheme from the continuous formulation. Results of numerical experiments show that the new scheme perform very well when compared with the exact solution and results from an earlier scheme.

Keywords: ill-conditioning; linear multistep methods; order; (non)singularity; underdetermined (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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