A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-differential equations with weakly singular kernels

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摘要

A spectral method based on operational matrices of the second kind Chebyshev polynomials (SKCPs) is employed for solving fractional integro-differential equations with weakly singular kernels. Firstly, properties of shifted SKCPs, operational matrix of fractional integration and product operational matrix are introduced and then utilized to reduce the given equation to the solution of a system of linear algebraic equations. This new approach provides a significant computational advantage by converting the given original problem to an equivalent linear Volterra integral equation of the second kind with the same initial conditions. Approximate solution is achieved by expanding the functions in terms of SKCPs and employing operational matrices. Unknown coefficients are determined by solving final system of linear equations. An estimation of the error is given. Finally, illustrative examples are included to demonstrate the high precision, fast computation and good performance of the new scheme.

论文关键词:26A33,45J05,45E10,65N35,Fractional integro-differential equation,Second kind Chebyshev polynomials,Operational matrix,Volterra integral equation

论文评审过程:Received 4 August 2015, Revised 26 April 2016, Available online 14 June 2016, Version of Record 23 June 2016.

论文官网地址:https://doi.org/10.1016/j.cam.2016.06.012