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

Rajat Singla; Gurjinder Singh; Higinio RamosV. KanwarAlessandro Della Corte

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

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

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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.

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2022年第21期|1.1-1.18|共18页
作者
Rajat Singla; Gurjinder Singh; Higinio RamosV. KanwarAlessandro Della Corte;
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Department of Mathematical Sciences I. K. Gujral Punjab Technical University Jalandhar Main Campus Kapurthala-144603 Punjab ||Department of Mathematics Akal University Bathinda-151302;

Department of Mathematical Sciences I. K. Gujral Punjab Technical University Jalandhar Main Campus Kapurthala-144603 Punjab;

Scientific Computing Group Universidad de Salamanca Plaza de la Merced 37008 Salamanca ||Escuela Politécnica Superior de Zamora Campus Viriato 49022 ZamoraUniversity Institute of Engineering and Technology Panjab University Chandigarh-160014;

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

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