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A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods

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  • F. Z. Geng
  • X. M. Li

Abstract

We introduce a new method for solving Riccati differential equations, which is based on reproducing kernel method and quasilinearization technique. The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differential equations are treated by using reproducing kernel method. The solutions of Riccati differential equations obtained using many existing methods give good approximations only in the neighborhood of the initial position. However, the solutions obtained using the present method give good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results compared with other methods show that the method is simple and effective.

Suggested Citation

  • F. Z. Geng & X. M. Li, 2012. "A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:603748
    DOI: 10.1155/2012/603748
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    References listed on IDEAS

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    1. Odibat, Zaid & Momani, Shaher, 2008. "Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 167-174.
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    1. Yulan Wang & Shuai Lu & Fugui Tan & Mingjing Du & Hao Yu, 2013. "Solving a Class of Singular Fifth‐Order Boundary Value Problems Using Reproducing Kernel Hilbert Space Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yu-Lan Wang & Hao Yu & Fu-Gui Tan & Shanshan Qu, 2014. "Solving a Class of Singularly Perturbed Partial Differential Equation by Using the Perturbation Method and Reproducing Kernel Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Reza Mokhtari & Fereshteh Toutian Isfahani & Maryam Mohammadi, 2012. "Reproducing Kernel Method for Solving Nonlinear Differential‐Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Dumitru Baleanu & Mohsen Alipour & Hossein Jafari, 2013. "The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann‐Liouville Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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