Mathematics and Computational Sciences

A Comparative Analysis of Daftardar–Gejji and Jafari Method and Chebyshev Least Squares Method in Solving Volterra Integro-Differential Equations

Articles in Press

Document Type : Original Article

Authors

Maria Rahman
Dipta Roy
Faria Tasnim
Tania Sharmin Khaleque

Department of Applied Mathematics, University of Dhaka, Dhaka 1000, Bangladesh

https://doi.org/10.30511/mcs.2026.2073962.1491
Abstract
This study presents a comparative analysis of two efficient numerical approaches for solving linear
and 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 employs
shifted Chebyshev polynomial approximations together with least-squares minimization to obtain
highly accurate spectral solutions. Convergence and stability properties of both methods are briefly
discussed within fixed-point and weighted residual frameworks. Several benchmark first- through
fourth-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 published
methods. Comparative analyses based on absolute error, L∞-norm, residual behavior, and CPU
time are presented to examine the convergence, computational efficiency, and numerical stability
of the proposed methods.

Keywords

Volterra Integro-Differential equation
Daftardar&ndash
Gejji and Jafari method
Chebyshev Least Squares method
Shifted Chebyshev polynomial
Computational stability analysis
Subjects
Mathematics and Computational Sciences

Articles in Press, Accepted Manuscript
Available Online from 19 June 2026

  • Receive Date 09 October 2025
  • Revise Date 13 June 2026
  • Accept Date 17 June 2026

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