用香农小波变换矩阵法近似求解分数阶微分方程

J. Iqbal, R. Abass, Puneet Kumar
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引用次数: 0

摘要

许多物理问题经常由分数阶微分方程控制,获得这些方程的解是近年来许多研究的主题。本文的目的是提出一种基于Shannon小波运算矩阵的分数阶积分方法。首先介绍了香农小波理论及其性质。采用块脉冲函数和配置法推导了构造这些运算矩阵的一般步骤。该方法的主要特点是将给定的问题压缩成一个代数方程组,可以很容易地用MATLAB软件包求解。通过数值算例分析了所设计方案的适用性、可靠性和有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximate solution of fractional differential equations using Shannon wavelet operational matrix method
Many physical problems are frequently governed by fractional differential equations and obtaining the solution of these equations have been the subject of a lot of investigations in recent years. The aim of this paper is to propose a novel and effective method based on Shannon wavelet operational matrices of fractional-order integration. The theory of Shannon wavelets and its properties are first presented. Block Pulse functions and collocation method are employed to derive a general procedure in constructing these operational matrices. The main peculiarity of the proposed technique is that it condenses the given problem into a system of algebraic equations that can be easily solved by MATLAB package. Furthermore, a designed scheme is applied to numerical examples to analyse its applicability, reliability, and effectiveness.
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