Galerkin Finite Element Methods for Linear Volterra Integro- Differential Systems in the Complex Plane
Abstract
In this manuscript, we present a finite element approach for numerically solving linear systems of Volterra integro-differential equations (LSVIDEs) of the second kind. First, we formulate the variational form of the linear system in the complex plane, establish the existence and uniqueness of its solution, and demonstrate through error analysis that the Galerkin finite element approximation converges to the exact solution of the LSVIDEs with order O(hr ). Furthermore, we present numerical examples to evaluate the performance of the proposed method, confirming that the method attains the optimal convergence order of O(hp+1) for smooth solutions.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Differential Equations and Boundary Problems
Numerical methods for differential equations
Publication details
- Journal / source
- The Saudi Journal of Applied Sciences and Technology
- Volume
- 2
- Issue
- 1
- Publication date
- 11 February 2026
- Language
- EN