信息与计算科学-多项分数阶常微分方程的数值微分法论文VIP专享

多项分数阶常微分方程的数值微分法摘要 在最近几年，多项分数阶常微分方程的数值微分法在许多数学模型领域有着十分重要的作用，并且在生活中以及许多科学和工程领域也都有着不可忽视的重要意义。并且多项分数阶常微分方程的数值微分法也是近几年来很多科研人员以及学者一直在努力研究的非常重要重要的部分。本文主要是通过函数逼近的方法研究并解决多项分数阶常微分方程的数值微分问题，通过函数逼近方法来解决问题之前我们需要了解函数逼近的许多定义。最后来研究解决多项分数阶常微分方程的数值微分问题。我将这篇文章分成了三个部分，第一部分主要介绍文章中所涉及的相关定义及性质，包括函数逼近的定义与性质和非线性方程的解法。第二部分主要讨论多项分数阶常微分方程的数值微分法。通过我们的预备知识用基于 L1 逼近的数值解法，基于 L1 逼近的线性化数值解法。然后可以继续求解数值算例的数值解以及精确解来证明算法的正确性与有效性。第三部分为 MATLAB 实现的具体代码。关键词：函数逼近 常微分方程 数值微分法 非线性方程Numerical differentiation of fractional order ordinary differential equationAbstract In recent years, the numerical differentiation of multiple fractional ordinary differential equations has played a very important role in many fields of mathematical models, and also has an important significance in life and many fields of science and engineering. And the numerical differentiation method of multiple fractional ordinary differential equations is also a very important part that many researchers and scholars have been trying to study in recent years.In this paper, we mainly study and solve the numerical differential problems of many fractional order ordinary differential equations by the method of function approximation. Before we solve the problems by the method of function approximation, we need to understand many definitions of function approximation. Finally, we study the numerical differentiation of multiple fractional ordinary differential equations. I divided this pa...