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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

WoS  JIF 2026 : 0.5 (Q3)

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Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

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Journal of Dynamical Systems and Geometric Theories
Open Access Research Article

Solution of Singularly Perturbed Boundary Value Problems with Singularity Using Variable Mesh Finite Difference Method

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pp. 113–124Vol. 19Issue 1January 2021DOI: 10.1080/1726037X.2021.1966945XML
Received:
06 Jun 2020
Accepted:
12 Jan 2021
Published Online:
29 Sep 2021
Article type:
Research Article
Language:
EN
Article no.:
1726037X.2021.1966945
Pages:
113–124

Abstract

We use non-polynomial spline with variable mesh to establish a numerical scheme for the solution of boundary value problem with singularity. The discrete equation of the problem is developed based on the condition of the class C1 of non-polynomial spline at the inner nodes and it is not valid for singularity. At singularity t = 0, the problem is modified in order to have a three term relationship. The method’s tridiagonal scheme is analyzed using the well-known discrete imbedding invariant algorithm. We discuss the error analysis of the scheme and two examples with layer at one end of the boundary are consider to demonstrate the practical utility of the scheme. Maximum absolute errors are present in tabular form to show the efficiency of the proposed method.

Keywords

Singularly perturbed two point singular boundary value problemInterior nodesSingular pointNon-polynomial splineBoundary layer

Subject Classifications

65L1065L1165L12

References

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