A Comparative Study Of Two Computational Techniques for Volterra-Fredholm Integro-Differential Equations

This paper presents a comparative study between two numerical techniques, namely, least squares and collocation methods, for solving Volterra-Fredholm Integro-Differential Equations (VFIDEs). The computations employ first-kind Chebyshev polynomials as basis functions, which transform VFIDEs into a system of linear algebraic equations with unknown Chebyshev coefficients. Matrix inversion is employed to solve the resulting system. The accuracy and efficiency of the techniques are assessed through numerical examples, with tables to aid the analysis. The results demonstrate that the collocation approach outperforms the least squares method. The calculations are carried out using Maple 18 software.