A new approach for solving Bratu’s problem-Reference-Cited by-同舟云学术

A new approach for solving Bratu’s problem

Published:2019-01-01 Issue:1 Volume:52 Page:336-346
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Ghomanjani Fateme¹,Shateyi Stanford²

Affiliation:

1. Department of Mathematics, Kashmar Higher Education Institute , Kashmar , Iran ; E-mail: fatemeghomanjani@gmail.com

2. Department of Mathematics , University of Venda , P Bag X5050, Thohoyandou 0950 , South Africa

Abstract

Abstract A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are exhibited to verify the efficiency and accuracy of the proposed technique. In this sequel, the obtained error was shown between the proposed technique, Chebyshev wavelets, and Legendre wavelets. The results display that this technique is accurate.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2019-0023/pdf

Reference36 articles.

1. [1] Caglara H., Caglarb N., Özer M., B-spline method for solving Bratu’s problem, Int. J. Comput. Math., 2010, 87(8), 1885–1891

2. [2] Ascher U. M., Matheij R., Russell R. D., Numerical solution of boundary value problems for ordinary differential equations, SIAM, Philadelphia, 1995

3. [3] Boyd J. P., Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation, Appl. Math. Comput., 2003, 14, 189–200

4. [4] Buckmire R., Investigations of nonstandard Mickens-type finite-difference schemes for singular boundary value problems in cylindrical or spherical coordinates, Numer. Methods Partial Differ. Equ., 2003, 19(3), 380–398

5. [5] Mounim A. S., de Dormale B. M., From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem, Numer. Methods Partial Differ. Equ., 2006, 22(4), 761–775

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Bézier Curve Method to Compute Various Meniscus Shapes;ACS Omega;2023-04-18

2. Numerical simulation of Bratu’s problem using a new form of the Adomian decomposition technique;International Journal of Numerical Methods for Heat & Fluid Flow;2023-03-07

3. On a New Construction of Generalized q-Bernstein Polynomials Based on Shape Parameter λ;Symmetry;2021-10-12

4. Block Hybrid Third Derivative Nyström type Method for Bratu’s equation;Mathematics and Computers in Simulation;2021-07