Numerical solution for diffusion equations with distributed order in time using a Chebyshev collocation method

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• 作者：Maria Luí ; sa Morgado^a ; ^{luisam@utad.pt} ; Magda Rebelo^b ; ^{msjr@fct.unl.pt} ; Luis L. Ferrá ; s^c ; ^d ; ^{luis.ferras@dep.uminho.pt} ; Neville J. Ford^d ; ^{njford@chester.ac.uk}
• 关键词：Fractional differential equation ; Caputo derivative ; Diffusion equation ; Chebyshev polynomials ; Spectral methods ; Distributed order equation
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：114
• 期：Complete
• 页码：108-123
• 全文大小：743 K
• 卷排序：114

文摘

In this work we present a new numerical method for the solution of the distributed order time-fractional diffusion equation. The method is based on the approximation of the solution by a double Chebyshev truncated series, and the subsequent collocation of the resulting discretised system of equations at suitable collocation points. An error analysis is provided and a comparison with other methods used in the solution of this type of equation is also performed.