Solving second order two-point boundary value problems accurately by a third derivative hybrid block integrator

• Published in: Applied mathematics and computation Vol. 421; p. 126960
• Main Authors: Ramos, Higinio, Singh, Gurjinder
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.05.2022
• Subjects: Block scheme; Boundary value problems; Convergence; Optimization strategy; Ordinary differential equations; Ordinary differential equations; Optimization strategy; Boundary value problems; Block scheme; Convergence
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.126960

•A hybrid block integrator for solving second order two-point boundary value problems is presented.•A theoretical analysis of the method has been done.•Some numerical experiments have been presented in order to illustrate good performance of the integrator. This article deals with the development of an optimized third-derivative hybrid block method for integrating general second order two-point boundary value problems (BVPs) subject to different types of boundary conditions (BCs) such as Dirichlet, Neumann or Robin. A purely interpolation and collocation approach has been used in order to develop the method. A constructive approach has been applied in the development of the method to consider two off-step optimal points among an infinite number of possible choices in a two-step block corresponding to a generic interval of the form [xn,xn+2]. The obtained method simultaneously produces an approximate solution over the entire integration interval. Some numerical experiments have been presented that show the good performance of the presented scheme.