A Family of A-Stable Optimized Hybrid Block Methods for Integrating Stiff Differential Systems. (16th May 2022)

• Record Type: Journal Article
• Authors: Singla, Rajat; Singh, Gurjinder; Ramos, Higinio; Kanwar, V.
• Other Names: Della Corte Alessandro Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2022(2022)
• Publication Date: 2022-05-16
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2022/5576891
• Languages: English
• ISSNs: 1024-123X

Abstract

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.