Numerical solution of third-kind Volterra integral equations with proportional delays based on moving least squares collocation method

Abstract

In this study, we propose a moving least squares approximation with shifted Chebyshev polynomials to solve linear and nonlinear third-kind Volterra delay integral equations (VDIEs). The suggested approach does not use meshing and does not rely on the geometry of the domain; therefore, we may consider it as a meshless method. This method approximates the solution using the collocation method based on the moving least squares approximation. The formulation of the technique for the suggested equations is described, and its convergence is analysed. Numerical results are presented to demonstrate the high resolution of the proposed approach and confirm its capability to provide accurate and efficient computations for Volterra delay integral equations of the third kind.

Keywords:

• Moving least square approximation
• nonlinear delayed volterra integral equations
• linear delayed volterra integral equations
• chebyshev polynomials
• collocation method
• error analysis

MSC 2020 AMS SUBJECT CLASSIFICATIONS:

• 45D05
• 45G10
• 65R20

Disclosure statement

No potential conflict of interest was reported by the author(s).