验证de Hoog算法数值求解亚扩散方程的有效性

反常输运现象广泛存在于生物和地质系统中.基于连续时间随机行走理论可以得到相应的反常输运方程,由于引入了分数阶算子,这些方程往往难以精确求解.de Hoog算法是一种数值Laplace逆变换算法.可以利用它可以来数值求解反常输运方程.反常输运中的亚扩散过程具有相对简单的方程,并在某些条件下可以精确求解,比较了这些精确解与通过de Hoog算法得到的数值解,验证了de Hoog算法的有效性,为使用该算法研究亚扩散和其它反常输运过程提供了更多的依据.

Validating the Reliability of the de Hoog Algorithm in Numerically Solving Sub-Diffusion Equations

Anomalous transport can be found in many biological and geological systems.Based on the continuous-time random walk theory,the corresponding anomalous transport equations can be obtained,which are generally difficult to be solved analytically due to the fractional operators.The de Hoog algorithm was developed for inversion of Laplace transforms,and it can be used to numerically solve the anomalous transport equations.To validate its reliability,we compare the numerical results with analytical solutions for sub-diffusion equations in some special cases;they are in good agreement.Our work thus gives credence to the reliability of the de Hoog algorithm in solving sub-diffusion and other anomalous transport equations.