A comparative analysis of Daftardar-Gejji and Jafari method and Chebyshev least squares method in solving Volterra integro-differential equations

This study presents a comparative analysis of two efficient numerical approaches for solving linearand nonlinear Volterra integro-differential equations: the Daftardar–Gejji and Jafari Method (DJM)and the Chebyshev Least Squares Method (CLSM). The Daftardar–Gejji and Jafari Method (DJM)provides robust results without linearization or perturbation assumptions, whereas CLSM employsshifted Chebyshev polynomial approximations together with least-squares minimization to obtainhighly accurate spectral solutions. Convergence and stability properties of both methods are brieflydiscussed within fixed-point and weighted residual frameworks. Several benchmark first- throughfourth-order VIDEs are solved to evaluate the performance of the proposed approaches. The ob-tained numerical results show excellent agreement with exact solutions and previously publishedmethods. Comparative analyses based on absolute error, L∞-norm, residual behavior, and CPUtime are presented to examine the convergence, computational efficiency, and numerical stabilityof the proposed methods.

کلیدواژه ها:

Volterra integro-differential equation ، Daftardar-Gejji and Jafari method ، Chebyshev Least Squares method ، Shifted Chebyshev polynomial ، Computational stability analysis