Numerical method to solve generalized nonlinear system of second order boundary value problems: Galerkin approach

Open Access

Original research article

Author(s):

Sadia Akter Lima^a, Md. Shafiqul Islam^b, Hazrat Ali^b, Md. Kamrujjaman^b

^a Department of Applied Mathematics, Noakhali Science and Technology University, Noakhali-3814, Bangladesh.
^b Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh.

Advances in the Theory of Nonlinear Analysis and its Applications 7(2), 280-291.

Received: July 5, 2022

Accepted: April 8, 2023

Published: April 9, 2023

Abstract

In this study, we consider the system of second-order nonlinear boundary value problems (BVPs). We focus on the numerical solutions of different types of nonlinear BVPs by the Galerkin finite element method (GFEM). First of all, we originate the generalized formulation of GFEM for those types of problems. Then we determine the approximate solutions of a couple of second-order nonlinear BVPs by GFEM. The numerical results are unfolded in tabular form and portrayed graphically along with the exact solutions. Those results demonstrate the applicability, compatibility, and accuracy of this scheme.

Keywords: Galerkin finite element method, nonlinear system of equations, higher-order nonlinear BVPs, trial function.

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APA Style

Lima, S. A., Islam, M. S., Ali, H., & Kamrujjaman, M. (2023). Numerical method to solve generalized nonlinear system of second order boundary value problems: Galerkin approach. Advances in the Theory of Nonlinear Analysis and its Application, 7(2), 280-291.