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Mathematical Sciences Letters
An International Journal


Volumes > Vol. 11 > No. 1


On the Numerical Solution of Volterra-Fredholm Integro-Differential Equations via Rational Chebyshev Spectral Collocation Approach

PP: 35-43
Mohamed A. Ramadan, Mahmoud A. Nassar, Mohamed A. Abd El salam,
The main purpose of this work is to examine the use of rational Chebyshev (RC) functions of the first kind to approximate the solution of high-order linear Fredholm-Volterra integro-differential equation (V-FIDE) under the mixed conditions. The RC functions are defined on a semi-infinite domain, so, the proposed V-FIDE is defined on the open interval [0, L] where 0 ≤ L < ∞. The definition of derivatives of the RC functions is used by means of total and truncated derivatives, which leads to two suggested schemes. The RC collocation method is used as a matrix discretization technique. The suggested V-FIDEs and their mixed conditions are converted to algebraic matrix equations, with unknown RC coefficients. The suggested technique deals with the kernels of the integral terms, in the double generalized form. A major advantage of the proposed method is that the approximate solution given by getting the RC coefficients very easily by using computer, especially if kernels are defined on an interval 0 ≤ x, t ≤ a < ∞. Illustrative four examples are utilized to betoken the applicability of the proposed method.

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