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

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  • Xiaomin Wang

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.

Suggested Citation

  • Xiaomin Wang, 2014. "A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, July.
    • Handle: RePEc:hin:jnljam:257049
    DOI: 10.1155/2014/257049
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    Cited by:

    1. Fathy, Mohamed & Abdelgaber, K.M., 2022. "Approximate solutions for the fractional order quadratic Riccati and Bagley-Torvik differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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