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Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients

机译：勒让德多项式运算矩阵法求解带变系数分数阶偏微分方程

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摘要

A numerical method for solving a class of fractional partial differential equations with variable coefficients based on Legendre polynomials is proposed. A fractional order operational matrix of Legendre polynomials is also derived. The initial equations are transformed into the products of several matrixes by using the operational matrix. A system of linear equations is obtained by dispersing the coefficients and the products of matrixes. Only a small number of Legendre polynomials are needed to acquire a satisfactory result. Results obtained using the scheme presented here show that the numerical method is very effective and convenient for solving fractional partial differential equations with variable coefficients.
机译：提出了一种基于勒让德多项式求解一类变系数分数阶偏微分方程的数值方法。还导出了勒让德多项式的分数阶运算矩阵。通过使用运算矩阵，将初始方程式转换为几个矩阵的乘积。通过分散系数和矩阵乘积获得线性方程组。仅需要少量的勒让德多项式即可获得令人满意的结果。使用这里提出的方案获得的结果表明，数值方法对于求解变系数分数阶偏微分方程是非常有效和方便的。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第10期|915195.1-915195.9|共9页
  • 作者

    Ma Yunpeng; Wang Lifeng; Yang Yongqiang;

  • 作者单位

    Beihang Univ, Sch Aeronaut Sci & Technol, Beijing 100191, Peoples R China.;

    Beihang Univ, Sch Aeronaut Sci & Technol, Beijing 100191, Peoples R China.;

    Beihang Univ, Sch Aeronaut Sci & Technol, Beijing 100191, Peoples R China.;

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