Galerkin Method and Its Residual Correction with Modified Legendre Polynomials

Authors

  • Md. Nurunnabi Sohel Department of Applied Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
  • Md. Shafiqul Islam Department of Applied Mathematics, University of Dhaka, Dhaka-1000, Bangladesh https://orcid.org/0000-0001-8031-0575
  • Md. Shariful Islam Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
  • Md. Kamrujjaman Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh https://orcid.org/0000-0002-4892-745X

DOI:

https://doi.org/10.37256/cm.3220221385

Keywords:

galerkin method, linear and nonlinear BVP, modified legendre polynomials, residual correction

Abstract

Accuracy and error analysis is one of the significant factors in computational science. This study employs the Galerkin method to solve second order linear or nonlinear Boundary Value Problems (BVPs) of Ordinary Differential Equations (ODEs) with modified Legendre polynomials to seek numerical solutions. The residual function of a differential operator is used as non-homogeneous term information of an error differential equation. The Galerkin approximation is then improved or corrected by solving the error differential equation by the Galerkin method using the same polynomials. Thus we apply the double layer Galerkin method to a variety of instances. We compare approximate solutions with exact ones and results available in the literature, and in every case, we find better accuracy.

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Published

2022-05-06

How to Cite

1.
Md. Nurunnabi Sohel, Md. Shafiqul Islam, Md. Shariful Islam, Md. Kamrujjaman. Galerkin Method and Its Residual Correction with Modified Legendre Polynomials. Contemporary Mathematics [Internet]. 2022 May 6 [cited 2022 May 20];3(2):188-202. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1385