A Comparative Study Of Two Computational Techniques for Volterra-Fredholm Integro-Differential Equations
Authors:
- 2 April 2024
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 1-6
Abstract
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.Keywords
This publication has 19 references indexed in Scilit:
- Legendre spectral element method for solving Volterra-integro differential equationsResults in Applied Mathematics, 2020
- A projection method for linear Fredholm–Volterra integro-differential equationsJournal of Taibah University for Science, 2019
- Dynamical behavior of integro-differential boundary value problem arising in nano-structures via Cellular Nanoscale Network approachJournal of Computational and Applied Mathematics, 2019
- Improved Bessel collocation method for linear Volterra integro-differential equations with piecewise intervals and application of a Volterra population modelApplied Mathematical Modelling, 2016
- Bernstein series solution of a class of linear integro-differential equations with weakly singular kernelApplied Mathematics and Computation, 2011
- Fourth order integro-differential equations using variational iteration methodComputers & Mathematics with Applications, 2007
- A Chebyshev polynomial approach for linear Fredholm–Volterra integro-differential equations in the most general formApplied Mathematics and Computation, 2006
- Adomian decomposition method for solving BVPs for fourth-order integro-differential equationsJournal of Computational and Applied Mathematics, 2006
- Solving linear integro-differential equations system by using rationalized Haar functions methodApplied Mathematics and Computation, 2004
- Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equationsApplied Mathematics and Computation, 2004