TY - JOUR AU - Md. Nurunnabi Sohel, AU - Md. Shafiqul Islam, AU - Md. Shariful Islam, AU - Md. Kamrujjaman, PY - 2022/05/06 Y2 - 2024/03/29 TI - Galerkin Method and Its Residual Correction with Modified Legendre Polynomials JF - Contemporary Mathematics JA - Contemp. Math. VL - 3 IS - 2 SE - Research Article DO - 10.37256/cm.3220221385 UR - https://ojs.wiserpub.com/index.php/CM/article/view/1385 SP - 188-202 AB - <p>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.</p> ER -