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2014 A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations
Xiaomin Wang
J. Appl. Math. 2014(SI13): 1-8 (2014). DOI: 10.1155/2014/257049


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.


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Xiaomin Wang. "A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations." J. Appl. Math. 2014 (SI13) 1 - 8, 2014.


Published: 2014
First available in Project Euclid: 1 October 2014

zbMATH: 07131452
MathSciNet: MR3240613
Digital Object Identifier: 10.1155/2014/257049

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI13 • 2014
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