Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2014), Article ID 257049, 8 pages.

A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations

Xiaomin Wang

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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.

Article information

Source
J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 257049, 8 pages.

Dates
First available in Project Euclid: 1 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1412178024

Digital Object Identifier
doi:10.1155/2014/257049

Mathematical Reviews number (MathSciNet)
MR3240613

Citation

Wang, Xiaomin. A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations. J. Appl. Math. 2014, Special Issue (2014), Article ID 257049, 8 pages. doi:10.1155/2014/257049. https://projecteuclid.org/euclid.jam/1412178024


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