$L$-stable block integrator from continuous midpoint method for solving differential equations

Articles in Press

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Natural Sciences, University of Jos, Plateau State, Nigeria

2 Department of Statistics, Federal College of Forestry, Jos, Nigeria

Abstract

In this paper, a stable block integrator was derived from continuous formulation of midpoint method for numerical solutions of differential equations with focus on predator-prey system and Oregonator model. The newly derived block method was consistent, zero stable and convergent. Further analysis of the method indicated that it is $A$-stable and also satisfies a highly desirable property; it is $L$-stable. Its implementation on predator-prey and highly stiff Oregonator model showed that it competes favourably with in-built Matlab ode23s which had been designed for stiff problems. This study helped to solve problems of instability usually associated with explicit midpoint method especially when used to solve stiff problems; also difficulty associated with the use of inappropriate method to kick-start midpoint method was addressed using block method approach. Compact outlook of the newly developed block method underscores its ease of implementation.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 08 November 2025

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