A Chebyshev Polynomial Approach for High-Order Linear Fredholm-Volterra Integro-Differential Equations

gamze YUKSEL, Mustafa GULSU, Mehmet SEZER
1.584 514

Abstract


The purpose of this study is to present a method for solving high order linear Fredholm-Volterra integro-differential equations in terms of Chebyshev polynomials under the mixed conditions. The method is based on the approximation by the truncated Chebyshev series. The higher order linear Fredholm-Volterra integro-differential equations and the conditions are transformed into the matrix equations, which corresponds to a system of linear algebraic equations with the unknown Chebyshev coefficients. Combining these matrix equations and then solving the system yields the Chebyshev coefficients of the solution function. Finally, the effectiveness of the method is illustrated in several numerical experiments and error analysis is performed.

 

Keywords: Chebyshev polynomials, Fredholm-Volterra integral equations, Polynomial approximations

 



Keywords


Chebyshev polynomials, Fredholm-Volterra integral equations, Polynomial approximations

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