A Family of A-Stable Optimized Hybrid Block Methods for Integrating Stiff Differential Systems

Rajat Singla, Gurjinder Singh, Higinio Ramos, V. Kanwar and Alessandro Della Corte

Mathematical Problems in Engineering, 2022, vol. 2022, 1-18

Abstract: In this article, a family of one-step hybrid block methods having two intrastep points is developed for solving first-order initial value stiff differential systems that occur frequently in science and engineering. In each method of the family, an intrastep point controls the order of the main method and a second one has a control over the stability features of the method. The approach used to develop the class of A-stable methods is based on interpolation and collocation procedures. The methods exhibit hybrid nature and produce numerical solutions at several points simultaneously. These methods can also be formulated as Runge-Kutta (RK) methods. Comparisons between the RK and block formulations of the proposed methods reveal a better performance of the block formulation in terms of computational efficiency. Furthermore, the efficiency of the methods is improved when they are formulated as adaptive step-size solvers using an error-control approach. Some methods of the proposed class have been tested to solve some well-known stiff differential systems. The numerical experiments show that the proposed family of methods performs well in comparison with some of the existing methods in the scientific literature.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:5576891

DOI: 10.1155/2022/5576891

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