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Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

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  • S. Balaji

Abstract

A Legendre wavelet operational matrix method (LWM) is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.

Suggested Citation

  • S. Balaji, 2014. "Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-10, June.
    • Handle: RePEc:hin:jijmms:304745
    DOI: 10.1155/2014/304745
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    References listed on IDEAS

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    4. Muhammad Jamil & Najeeb Alam Khan, 2011. "Slip Effects on Fractional Viscoelastic Fluids," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-19, December.
    5. Mehmet Merdan, 2012. "On the Solutions Fractional Riccati Differential Equation with Modified Riemann-Liouville Derivative," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-17, May.
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