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  • 标题:A fast numerical method for fractional partial differential equations
  • 本地全文:下载
  • 作者:S. Mockary ; E. Babolian ; A. R. Vahidi
  • 期刊名称:Advances in Difference Equations
  • 印刷版ISSN:1687-1839
  • 电子版ISSN:1687-1847
  • 出版年度:2019
  • 卷号:2019
  • 期号:1
  • 页码:1-20
  • DOI:10.1186/s13662-019-2390-z
  • 出版社:Hindawi Publishing Corporation
  • 摘要:In this paper, we use operational matrices of Chebyshev polynomials to solve fractional partial differential equations (FPDEs). We approximate the second partial derivative of the solution of linear FPDEs by operational matrices of shifted Chebyshev polynomials. We apply the operational matrix of integration and fractional integration to obtain approximations of (fractional) partial derivatives of the solution and the approximation of the solution. Then we substitute the operational matrix approximations in the FPDEs to obtain a system of linear algebraic equations. Finally, solving this system, we obtain the approximate solution. Numerical experiments show an exponential rate of convergence and hence the efficiency and effectiveness of the method.
  • 关键词:System of fractional differential equations; Operational matrices; Chebyshev polynomials; Caputo-fractional derivative; Fractional partial differential equations
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