Spline collocation method for solving the third-kind Volterra integral equations

Davari, Ali

doi:10.22075/ijnaa.2024.35545.5287

Spline collocation method for solving the third-kind Volterra integral equations

Articles in Press

Document Type : Research Paper

Author

Ali Davari

Department of Mathematics, Khansar Campus, University of Isfahan, Iran.

10.22075/ijnaa.2024.35545.5287

Abstract

In this paper, we consider the Volterra integral equations (VIEs) of the third kind. A procedure, using spline functions, for obtaining
approximate solutions to Volterra integral equations of the third kind is presented. We develop an efficient spline collocation method for solving this type of equations. The proposed scheme is especially suited for VIEs in polynomial spline space, due to its essential feature of local approximations on subintervals. We then use these results in the convergence analysis of a polynomial spline collocation method for solving such problems numerically. The solvability of spline collocation methods is accessed, and the convergence analysis is studied. Numerical results confirm the spectral accuracy and the theoretical results of the proposed method.

Keywords

The third-kind Volterra functional integral equations

Spline collocation method

Convergence analysis