A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations
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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/257049 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850230539986927616 |
|---|---|
| author | Xiaomin Wang |
| author_facet | Xiaomin Wang |
| author_sort | Xiaomin Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-28c812debcab4bee86609ee747bd78f0 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-28c812debcab4bee86609ee747bd78f02025-08-20T02:03:51ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/257049257049A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential EquationsXiaomin Wang0School of Engineering, Huazhong Agricultural University, Wuhan, Hubei 430070, ChinaA 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.http://dx.doi.org/10.1155/2014/257049 |
| spellingShingle | Xiaomin Wang A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations Journal of Applied Mathematics |
| title | A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations |
| title_full | A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations |
| title_fullStr | A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations |
| title_full_unstemmed | A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations |
| title_short | A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations |
| title_sort | coiflets based wavelet laplace method for solving the riccati differential equations |
| url | http://dx.doi.org/10.1155/2014/257049 |
| work_keys_str_mv | AT xiaominwang acoifletsbasedwaveletlaplacemethodforsolvingthericcatidifferentialequations AT xiaominwang coifletsbasedwaveletlaplacemethodforsolvingthericcatidifferentialequations |