A New Numerical Algorithm for Solving a Class of Fractional Advection-Dispersion Equation with Variable Coefficients Using Jacobi Polynomials

A. H.Bhrawy

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A New Numerical Algorithm for Solving a Class of Fractional Advection-Dispersion Equation with Variable Coefficients Using Jacobi Polynomials

机译：利用雅可比多项式求解一类变系数分数阶对流弥散方程的新数值算法

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We propose Jacobi-Gauss-Lobatto collocation approximation for the numerical solution of a class of fractional-in-space advection-dispersion equation with variable coefficients based on Caputo derivative. This approach has the advantage of transforming the problem into the solution of a system of ordinary differential equations in time this system is approximated through an implicit iterative method. In addition, some of the known spectral collocation approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parametersαandβ. Finally, numerical results are provided to demonstrate the effectiveness of the proposed spectral algorithms.

机译：针对一类基于Caputo导数的变系数空间对流对流扩散方程的数值解，我们提出了雅可比-高斯-洛巴托搭配近似方法。这种方法的优点是可以通过隐式迭代方法将问题及时转换为常微分方程组的解。此外，如果我们适当地选择Jacobi参数α和β的相应特殊情况，则可以从我们的算法中得出某些已知的光谱搭配近似值作为特殊情况。最后，提供数值结果以证明所提出的频谱算法的有效性。

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《Abstract and applied analysis》 |2013年第14期|共9页
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A. H.Bhrawy;
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A New Numerical Algorithm for Solving a Class of Fractional Advection-Dispersion Equation with Variable Coefficients Using Jacobi Polynomials

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