Finite Element Methods via Cubic Hermite Shape Functions for a Singularly Perturbed Boundary Value Problem with Mixed Shifts

Vivek Krishnamoorthy; Nageshwar Rao Ragi

doi:10.5269/bspm.78878

Mr. Vivek K Vellore Institute of Technology, Vellore https://orcid.org/0000-0002-4251-7564
Dr. R. Nageshwar Rao Vellore Institute of Technology, Vellore https://orcid.org/0000-0003-4225-1927

Abstract

In this paper, Galerkin finite element method is developed for a singularly perturbed differential equation with mixed shifts. Fitted operator and fitted mesh approaches are utilized for discretization. Cubic Hermite shape functions are chosen as basis functions in developing the method. Comparison of maximum absolute errors for the solutions of test problems is done for the proposed methods. Graphs are plotted to demonstrate the effect of shifts on the solution of the problem.

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Author Biographies

Mr. Vivek K, Vellore Institute of Technology, Vellore

Mr. Vivek K is a full time research scholar in the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India.

Dr. R. Nageshwar Rao , Vellore Institute of Technology, Vellore

Dr. R. Nageshwar Rao is an Associate Professor in the Department of Mathematics, School of Advanced Sciences. He also serves as Associate Professor in the Department of Database Systems, School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, India.