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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 9 > No. 2


Spectral Legendre-Chebyshev Treatment of 2D Linear and Nonlinear Mixed Volterra-Fredholm Integral Equation

PP: 37-47
R. M. Hafez, Y. H. Youssri,
A numerical algorithm to handle the 2D mixed Volterra-Fredholm integral equations (MV-FIEs) is introduced. The fundamentals of shifted Legendre and shifted Chebyshev polynomials are first mentioned. These fundamentals jointly with the shifted Gauss-Legendre and Chebyshev nodes are then used to transform the integral equations to matrix equation. The main advantages of the presented scheme is its reasonable accuracy. Sequentially, fine numerical results can be obtained via a relatively few number of collocation points. The convergence and error analyses of the method were discussed in detail. Numerical test experiments are offered to demonstrate the validity, efficiency, and applicability of the scheme.

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