时间分数阶微分方程的数值解法摘要 近年来，随着计算工具的更新迭代，分数阶微分方程在生活中的应用也更为广泛，如材料学，金融经济学，物理力学，生物遗传学等。在微分方程的解析解实用性不强的客观环境下,分数阶微分方程的数值解法就成为人们关注的重点。这篇论文的主要目的就是为了介绍一种方便准确的求解时间分数阶微分方程的数值方法。然后运用 MATLAB 软件去检验此算法的准确性并进行误差分析。为了更好的描述这个算法，我将整篇论文分成了三个部分，第一部分主要就是描述微积分方程相关的定义定理，Caputo 导数,Riemann-Liouville 积分和微积分算子的定义定理。第二部分就是时间分数阶方程数值解法的具体实现，主要分为两个步骤，首先用微积分算子的相关定理得到等价方程，在运用数值逼近中心离散的方法离散方程。第三部分为数值实验，求解数值算例，来验证此数值算法的有效性，并进行误差分析。数值实验表明，运算所得出的精确解和数值解误差较小，该算法准确性较高。 关键词 分数阶微分方程 Caputo 导数 Riemann-Liouville 积分 数值逼近 中心离散第 I 页The numerical solution of the time fractional differential equationAbstract With the continuous upgrade of calculation tools in recent years, the application of fractional differential equations becomes more widespread in different areas of our life, such as financial economics, materials sciences, genetics, physics, and other research fields. Given the objective situation that the analytical solution of differential equation is not practical, researchers are now focusing on the numerical solution of fractional differential equation. The main aim of this paper is to introduce a simple and accurate way to solve fractional differential equation, check the accuracy of this arithmetic using MATLAB and conduct error analysis at the end.To better describe this arithmetic, this paper is structured into three parts. The first part mainly describes the definition and related theorems of the calculus equation, the derivative of Caputo, Riemann-Lio...
