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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 603748, 8 pages
http://dx.doi.org/10.1155/2012/603748
Research Article

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

Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China

Received 1 December 2011; Accepted 17 December 2011

Academic Editor: Shaher Momani

Copyright © 2012 F. Z. Geng and X. M. Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [9 citations]

The following is the list of published articles that have cited the current article.

  • Reza Mokhtari, Fereshteh Toutian Isfahani, and Maryam Mohammadi, “Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations,” Abstract and Applied Analysis, vol. 2012, pp. 1–10, 2012. View at Publisher · View at Google Scholar
  • Dumitru Baleanu, Mohsen Alipour, and Hossein Jafari, “The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann-Liouville Derivative,” Abstract and Applied Analysis, vol. 2013, pp. 1–7, 2013. View at Publisher · View at Google Scholar
  • Yulan Wang, Shuai Lu, Fugui Tan, Mingjing Du, and Hao Yu, “Solving a Class of Singular Fifth-Order Boundary Value Problems Using Reproducing Kernel Hilbert Space Method,” Abstract and Applied Analysis, vol. 2013, pp. 1–6, 2013. View at Publisher · View at Google Scholar
  • Yu-Lan Wang, Hao Yu, Fu-Gui Tan, and Shanshan Qu, “Solving a Class of Singularly Perturbed Partial Differential Equation by Using the Perturbation Method and Reproducing Kernel Method,” Abstract and Applied Analysis, vol. 2014, pp. 1–5, 2014. View at Publisher · View at Google Scholar
  • Maryan Mohammadi, “A Reproducing Kernel Method for Solving a Class of Nonlinear Systems of PDEs,” Mathematical Modelling and Analysis, vol. 19, no. 2, pp. 180–198, 2014. View at Publisher · View at Google Scholar
  • Mojtaba Fardi, Reza Khoshsiar Ghaziani, and Mehdi Ghasemi, “The reproducing kernel method for some variational problems depending on indefinite integrals,” Mathematical Modelling and Analysis, vol. 21, no. 3, pp. 412–429, 2016. View at Publisher · View at Google Scholar
  • S. Vahdati, M. Fardi, and M. Ghasemi, “Option pricing using a computational method based on reproducing kernel,” Journal of Computational and Applied Mathematics, 2017. View at Publisher · View at Google Scholar
  • K. Sayevand, and H. Jafarian, “Solving Integro-differential Equation with an Integral Boundary Condition Using the Reproducing Kernel,” International Journal of Applied and Computational Mathematics, 2017. View at Publisher · View at Google Scholar
  • Mehmet Giyas Sakar, “Iterative reproducing kernel Hilbert spaces method for Riccati differential equations,” Journal of Computational and Applied Mathematics, vol. 309, pp. 163–174, 2017. View at Publisher · View at Google Scholar