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- Title
A fitted operator numerical method for singularly perturbed Fredholm integro-differential equation with integral initial condition.
- Authors
Oljira, Aklilu Fufa; Woldaregay, Mesfin Mekuria
- Abstract
Objectives: In this paper, a uniformly convergent numerical scheme is proposed for solving a singularly perturbed Fredholm integro-differential equation with an integral initial condition. The equation involves a left boundary layer which makes it difficult to solve it using the standard numerical methods. A fitted operator finite difference method is used to approximate the differential part of the equation and the composite Simpson 1 3 rule is used for the integral parts of the equation and the initial condition. Result: The stability bound and error estimation of the approximated solution are performed, to show the uniform convergence of the scheme with order one in the maximum norm. Numerical test examples are provided to calculate the maximum absolute errors, thrgence, and the uniform error for a couple of examples to support theoretical analysis.
- Subjects
INTEGRAL equations; FREDHOLM equations; INTEGRO-differential equations; DIFFERENTIAL equations; FINITE difference method; BOUNDARY layer (Aerodynamics)
- Publication
BMC Research Notes, 2024, Vol 17, Issue 1, p1
- ISSN
1756-0500
- Publication type
Article
- DOI
10.1186/s13104-023-06649-9