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

Higinio Ramos and Gurjinder Singh

Applied Mathematics and Computation, 2022, vol. 421, issue C

Abstract: 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.

Keywords: Ordinary differential equations; Boundary value problems; Block scheme; Convergence; Optimization strategy (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000467

DOI: 10.1016/j.amc.2022.126960

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