One-Step Hybrid Block Method Containing Third Derivatives and Improving Strategies for Solving Bratu's and Troesch's Problems
Year: 2020
Author: Higinio Ramos, Mufutau Ajani Rufai, Higinio Ramos
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 946–972
Abstract
In this paper, we develop a one-step hybrid block method for solving boundary value problems, which is applied to the classical one-dimensional Bratu's and Troesch's problems. The convergence analysis of the new technique is discussed, and some improving strategies are considered to get better performance of the method. The proposed approach produces discrete approximations at the grid points, obtained after solving an algebraic system of equations. The solution of this system is obtained through a homotopy-type strategy used to provide the starting points needed by Newton's method. Some numerical experiments are presented to show the performance and effectiveness of the proposed approach in comparison with other methods that appeared in the literature.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2019-0157
Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 946–972
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Ordinary differential equations Bratu's problem Troesch's problem boundary value problems hybrid block method homotopy-type strategy.
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