Convergence analysis of the homogeneous second order difference method for a singularly perturbed Volterra delay-integro-differential equation
Chaos, Solitons and Fractals, vol.150, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 150
- Publication Date: 2021
- Doi Number: 10.1016/j.chaos.2021.111100
- Journal Name: Chaos, Solitons and Fractals
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
- Keywords: Volterra delay-integro-differential equation, Singular perturbation, Finite difference method, Uniform convergence, LINEAR MULTISTEP METHODS, INTEGRODIFFERENTIAL EQUATIONS, STABILITY ANALYSIS, BEHAVIOR
- Erzincan Binali Yildirim University Affiliated: Yes
Abstract
© 2021 Elsevier LtdA linear Volterra delay-integro-differential equation with a singular perturbation parameter ε is considered. The problem is discretized using exponentially fitted schemes on the Shishkin type meshes. It is proved that the numerical approximations generated by this method are O(N−2lnN) convergent in the discrete maximum norm, where N is the mesh parameter. Numerical results show a good agreement with the theoretical analysis.