A novel second-order fitted computational method for a singularly perturbed Volterra integro-differential equation

ABSTRACT

In this paper, we deal with the second-order accurate homogeneous (non-hybrid) type difference scheme for solving a singularly perturbed first-order Volterra integro-differential equation. It is shown that the method displays uniform convergence of $O(N^{-2}\ln N)$ on a special non-uniform mesh, where N is the mesh parameter. Numerical results are included to verify the theoretical estimates.

KEYWORDS:

• Volterra integro-differential equation
• singular perturbation
• finite difference
• uniform convergence

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65L11
• 65L12
• 65L20
• 65R20

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ömer Yapman  http://orcid.org/0000-0003-3117-2932

Gabil M. Amiraliyev  http://orcid.org/0000-0001-6585-7353