On Collocation Methods for Solving First-Order Volterra Type Linear
Integro-Differential Equations
Author(s) : William Dunama, Ayinde Muhammed Abdullahi, Adewale Adeyemi James, Oyedepo Taiye
ABSTRACT:
The numerical solutions of linear Volterra-type integro-differential equations (VIDEs) have been considered in this paper. We propose using the third kind of Chebyshev polynomial as the basis function to approximate the solution of the problems using MAPLE 2018 software. Standard collocation points were chosen to collocate the approximate solution, and numerical experiments were performed on some sample problems already solved by the finite difference method and the method of power series as a basis polynomial, utilizing both the standard and Chebyshev-Gauss-Lobbatto collocation points. Furthermore, we compared our results to some previously published findings. Our proposed method yields superior approximate solutions and exhibits significantly lower absolute errors compared to the existing method. Furthermore, the absolute errors obtained are exceptionally minimal, indicating both convergence and computational efficiency.
KEYWORD(S):
Chebyshev polynomial, Collocation, Approximate solution and Volterra Integro-differential equation
