Volume 13, Issue 4
One-Step Hybrid Block Method Containing Third Derivatives and Improving Strategies for Solving Bratu's and Troesch's Problems

Mufutau Ajani Rufai & Higinio Ramos

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 946-972.

Published online: 2020-06

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  • 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.

  • Keywords

Ordinary differential equations, Bratu’s problem, Troesch’s problem, boundary value problems, hybrid block method, homotopy-type strategy.

  • AMS Subject Headings

65L10, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-13-946, author = {Mufutau Ajani Rufai , and Higinio Ramos , }, title = {One-Step Hybrid Block Method Containing Third Derivatives and Improving Strategies for Solving Bratu's and Troesch's Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {13}, number = {4}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0157}, url = {http://global-sci.org/intro/article_detail/nmtma/16961.html} }
TY - JOUR T1 - One-Step Hybrid Block Method Containing Third Derivatives and Improving Strategies for Solving Bratu's and Troesch's Problems AU - Mufutau Ajani Rufai , AU - Higinio Ramos , JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 946 EP - 972 PY - 2020 DA - 2020/06 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0157 UR - https://global-sci.org/intro/article_detail/nmtma/16961.html KW - Ordinary differential equations, Bratu’s problem, Troesch’s problem, boundary value problems, hybrid block method, homotopy-type strategy. AB -

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.

Mufutau Ajani Rufai & Higinio Ramos. (2020). One-Step Hybrid Block Method Containing Third Derivatives and Improving Strategies for Solving Bratu's and Troesch's Problems. Numerical Mathematics: Theory, Methods and Applications. 13 (4). 946-972. doi:10.4208/nmtma.OA-2019-0157
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