A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential EquationsReport as inadecuate




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Journal of Applied Mathematics - Volume 2014 2014, Article ID 257049, 8 pages -

Research ArticleSchool of Engineering, Huazhong Agricultural University, Wuhan, Hubei 430070, China

Received 28 January 2014; Accepted 1 July 2014; Published 15 July 2014

Academic Editor: Changbum Chun

Copyright © 2014 Xiaomin Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A wavelet iterative method based on a numerical integration by using the Coiflets orthogonal wavelets for a nonlinear fractional differential equation is proposed. With the help of Laplace transform, the fractional differential equation was converted into equivalent integral equation of convolution type. By using the wavelet approximate scheme of a function, the undesired jump or wiggle phenomenon near the boundary points was avoided and the expansion constants in the approximation of arbitrary nonlinear term of the unknown function can be explicitly expressed in finite terms of the expansion ones of the approximation of the unknown function. Then a numerical integration method for the convolution is presented. As an example, an iterative method which can solve the singular nonlinear fractional Riccati equations is proposed. Numerical results are performed to show the efficiency of the method proposed.





Author: Xiaomin Wang

Source: https://www.hindawi.com/



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