Comparative study of numerical methods for singularly perturbed boundary turning point problems with mixed boundary conditions

Document Type : Research Article

Authors

1 PG and Research Department of Mathematics, Seethalakshmi Ramaswami College( Affiliated to Bharathidasan University), Tiruchirapalli-2, Tamilnadu, India

2 Amrita School of Physical Science, Amrita Vishwa Vidyapeetham, Coimbatore, Tamilnadu, India

3 Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu, Tamilnadu India

4 Department of Mathematics, Bharathidasan University, Tiruchirappalli, India

Abstract

A comparative study on numerical methods for Singularly Perturbed Boundary Turning Point Problems (SPBTPPs) featuring discontinuous source terms are examined. The study involves developing and analyzing two specific numerical techniques: the finite difference method and a hybrid difference method incorporating a Shishkin-type mesh. This approach demonstrates notable capabilities, exhibiting almost first-order and second-order convergence for the finite difference and hybrid difference methods, respectively. Numerical results are given  to support the theoretical findings.

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Journal of Mathematical Modeling
Volume 13, Issue 3
July 2025
Pages 609-628

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