论文标题
不均匀的参数缩放和可变顺序分数扩散方程
Inhomogeneous parametric scaling and variable-order fractional diffusion equations
论文作者
论文摘要
我们讨论了以晶格连续时间随机行走方案的连续限制，其参数依赖于位置依赖性的晶格连续时间随机行走方案，其参数依赖于位置的晶格连续时间随机行走方案，讨论了Integ-Differentix方程（可变的时间折叠扩散方程）的推导和解。我们专注于宽大案例，并讨论两种情况作为示例：一个由两个具有不同指数尺寸指数的部分组成的系统，以及一个从间隔的一端线性变化为另一个区间的系统。在这两种情况下，我们都比较了将晶格上描述该过程的一般主方程的数值解与连续方程的相应解，该方程是通过使用Gaver-Stehfest algorithm的随后的数值反转的拉普拉斯域中相应方程的精确解。
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time probability density functions, whose parameters are position-dependent. We concentrate on subdiffusive cases and discuss two situations as examples: A system consisting of two parts with different exponents of subdiffusion, and a system in which the subdiffusion exponent changes linearly from one end of the interval to another one. In both cases we compare the numerical solutions of generalized master equations describing the process on the lattice with the corresponding solutions of the continuous equations, which follow by exact solution of the corresponding equations in the Laplace domain with subsequent numerical inversion using the Gaver-Stehfest algorithm.
