Rakesh Kumar, Kapil Kant, and B.V. Rathish Kumar
Numerical Solutions to the System of Linear Volterra Integral Equation with Mixed Type Kernels
Dynamic Systems and Applications 34 (2025)  117-131

https://doi.org/10.46719/dsa2025.34.06

ABSTRACT.
In this study, we propose the Jacobi Spectral Galerkin(JSG) and iterated Jacobi
Spectral Galerkin Methods for a system of Linear Volterra Integral Equations(VIE) for mixed type
kernels (weakly singular(WS) and smooth). We propose numerical approximation method for solving
the system of Volterra integral equation. We improve the order of convergence in iterated
Jacobi Spectral Galerkin method over Jacobi spectral Galerkin method. We will also give numerical
examples for verifying the theoretical outcomes.

AMS (MOS) Subject Classification. 54A20, 54A40, 54A45, 45F10, 45F15.

Key Words and Phrases. Volterra integral equation, Weakly singular kernel, mixed type kernels,
Galerkin method, Iterated Galerkin method.