Numerical Methods of Fractional Partial Differential Equations and Applications [分数阶偏微分方程数值方法及其应用]

Abstract

"LLC book introduces the theory and numerical methods in many areas of engineering and scientific research relating to fractional partial differential equations analysis results. most of these authors and their collaborators obtained research results. These fractional partial differential equations. including space. time. time - space fractional diffusion equation. fractional advection - diffusion equation of fractional reaction - diffusion equation. anomalous diffusion equation times. modified anomalous diffusion equation times. anomalous diffusion equation super. fractional Cable equation. including a number of time - space fractional partial differential equations and variational fractional partial differential equations..." -- <i>Amazon website</i>\ud \ud Abstract in Chinese:\ud \ud 本书主要介绍许多工程和科学研究领域中有关分数阶偏微分方程的数值方法及其理论分析的最新成果，这些内容大部分是作者及其合作者得到的研究成果。这些分数阶偏微分方程包括空间，时间，时间-空间分数阶扩散方程，分数阶对流-扩散方程，分数阶反应-扩散方程，反常次扩散方程，修正的反常次扩散方程，反常超扩散方程，分数阶Cable方程，也包括多项时间-空间分数阶偏微分方程和变分数阶偏微分方程。分数阶偏微分方程的数值方法及其理论分析包括有限差分方法，有限元方法，谱方法，有限体积方法，无网格方法。我们讨论了数值方法的稳定性和收敛性，给出了数值结果，同时我们也介绍分数阶偏微分方程的一些应用实例。 -- <i>当当图书</i