Numerical solution of high-order linear integro-differential equations with variable coefficients using two proposed schemes for rational Chebyshev functions

Year 2016, Volume: 4 Issue: 3, 22 - 35, 30.09.2016

Mohamed Ramadan Kamal Raslan Adel Hadhoud Mahmoud Nassar

Abstract

In this paper, a rational Chebyshev (RC) collocation
method is presented to solve high-order linear Fredholm integro-differential
equations with variable coefficients under the mixed conditions, in terms of RC
functions by two proposed schemes. The proposed method converts the integral
equation and its conditions to matrix equations, by means of collocation points
on the semi–infinite interval, which corresponding to systems of linear
algebraic equations in RC coefficients unknowns. Thus, by solving the matrix
equation, RC coefficients are obtained and hence the approximate solution is
expressed in terms of RC functions. Numerical examples are given to illustrate
the validity and applicability of the method. The proposed method numerically
compared with others existing methods as well as the exact solutions where it
maintains better accuracy.

Keywords

Rational Chebyshev functions, Collocation method

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