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2 Journal of Applied Mathematics and Computational Mechanics

2 2022

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Numerical study for a second order Fredholm integro-differential equation by applying Galerkin-Chebyshev-wavelets method

Henka Youcef, Lemita Samir, Aissaoui Mohamed-Zine

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 4

28--39

In the present paper, we apply the Galerkin method using Chebyshev wavelets to approximate the exact solution for a second order Fredholm integro-differential equation with initial conditions. This numerical method gives us a nonlinear algebraic system that would be solved using the Picard successive approximations technique. Furthermore, we show the validity and the ability of the proposed method through some illustrative examples.

Numerical solution of two-dimensional Fredholm integro-differential equations by Chebyshev integral operational matrix method

Ishola Christie Yemisi, Taiwo Omotayo Adebayo, Adebisi Ajimot Folasade, Peter Olumuyiwa James

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 1

29--40

This paper presents the Chebyshev Integral Operational Matrix Method (CIOMM) for the numerical solution of two-dimensional Fredholm Integro-Differential Equations (2D-FIDEs). The process of the method is obtaining the operational matrix of integration by evaluating a 2D integral of 2D Chebyshev polynomial basis functions and assuming approximate solutions of the 2D-FIDEs as a truncated 2D Chebyshev series. This leads to a system of linear algebraic equations which are solved to obtain the values of the unknown constants using Maple 18. Some numerical problems are solved to illustrate the practicability of the method.