Singularly perturbed two-point boundary value problem by applying exponential fitted finite difference method

Document Type : Research Article

Authors

• N. Kumar ¹
• R. Kumar Sinha ¹
• R. Ranjan ²

¹ Department of Mathematics, National Institute of Technology Patna, Patna - 800005, India.

² Department of Science and Technology, Bihar, Government Polytechnic, Lakhisarai, Lakhisarai- 811311, India.

10.22067/ijnao.2023.83070.1283

Abstract

The present study addresses an exponentially fitted finite difference method to obtain the solution of singularly perturbed two-point boundary value problems (BVPs) having a boundary layer at one end (left or right) point on uniform mesh. A fitting factor is introduced in the derived scheme using the theory of singular perturbations. Thomas algorithm is employed to solve the resulting tri-diagonal system of equations. The convergence of the presented method is investigated. Several model example problems are solved using the proposed method. The results are presented with terms of maximum absolute errors, which demonstrate the accuracy and efficiency of the method. It is observed that the proposed method is capable of producing highly accurate results with minimal computational effort for a fixed value of step size h, when the perturbation parameter tends to zero. From the graphs, we also observed that a numerical solution approximates the exact solution very well in the boundary layers for smaller value of ε.

Keywords

• Singular perturbation problem
• Stability and convergence
• Finite difference method

Main Subjects

• Numerical methods for differential equations and its applications

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