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

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 مرداد 1402

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2023.83070.1283

نویسندگان

Narendra Kumar^{* 1}؛ Rajesh Kumar Sinha¹؛ Rakesh Ranjan²

¹Department of Mathematics, National Institute of Technology Patna, 800005 Bihar, India

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

چکیده

The present study addresses an exponentially fitted finite difference method to obtain the solution of singularly perturbed two point boundary value problems(BVPs) having 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. Convergence of the presented method are investigated. Several model example problems are solved using the proposed method. The results are presented in 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 perturbation parameter tends to zero. From the graphs, we also observed that numerical solution approximate exact solution very well in the boundary layers for smaller value of 𝞮.

کلیدواژه‌ها

Singular perturbation problem؛ Stability and convergence؛ Finite difference method