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Original Articles

On the Solution of the Riccati Equation by the Decomposition Method

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Pages 103-109 | Published online: 15 Sep 2010

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Read on this site (4)

Şuayip Yüzbaşı. (2020) An operational method for solutions of Riccati type differential equations with functional arguments. Journal of Taibah University for Science 14:1, pages 661-669.
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Fateme Ghomanjani & Esmaile Khorram. (2017) Approximate solution for quadratic Riccati differential equation. Journal of Taibah University for Science 11:2, pages 246-250.
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Vedat Asil, Hasan Bulut & D. J. Evans. (2004) On the oscillatory solutions of nonlinear hyperbolic differential equations by the decomposition method . International Journal of Computer Mathematics 81:5, pages 639-645.
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Hasan Bulut & D. J. Evans. (2003) Oscillations Of Solutions Of Initial Value Problems For Parabolic Equations By The Decomposition Method. International Journal of Computer Mathematics 80:7, pages 863-868.
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Articles from other publishers (27)

Deniz Elmacı, Şuayip Yüzbaşı & Nurcan Baykuş Savaşaneril. (2023) Shifted Legendre method for solutions of Riccati type functional differential equations and application of RL circuit model . International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 37:2.
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Merve Yücel, O. Sh Mukhtarov & Kadriye Aydemir. (2022) Computation of eigenfunctions of nonlinear boundary-value -transmission problems by developing some approximate techniques. Boletim da Sociedade Paranaense de Matemática 41, pages 1-12.
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Khalid Hammood AL-Jizani & Suhartati. A modification of decomposition approach for solving non-linear quadratic differential equation; Theory and application. A modification of decomposition approach for solving non-linear quadratic differential equation; Theory and application.
F. Karimi, T. Allahviranloo, S. M. Pishbin & S. Abbasbandy. (2021) Solving Riccati Fuzzy Differential Equations. New Mathematics and Natural Computation 17:01, pages 29-43.
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O. P. Ogundile, S. O. Edeki & D. G. Olaniregun. (2021) Iterative methods for solving Riccati differential equations. Journal of Physics: Conference Series 1734:1, pages 012003.
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Şuayip Yüzbaşı & Gamze Yıldırım. (2020) Legendre Collocation Method to Solve the Riccati Equations with Functional Arguments. International Journal of Computational Methods 17:10, pages 2050011.
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Orestes Tumbarell Aranda & Fernando A. Oliveira. (2020) Analytical and Numerical Solutions of the Riccati Equation Using the Method of Variation of Parameters. Application to Population Dynamics. Journal of Computational and Nonlinear Dynamics 15:10.
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Fateme Ghomanjani & Stanford Shateyi. (2020) Solving a Quadratic Riccati Differential Equation, Multi-Pantograph Delay Differential Equations, and Optimal Control Systems with Pantograph Delays. Axioms 9:3, pages 82.
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Mohamed Z. Mohamed & Tarig M. Elzaki. (2020) Applications of new integral transform for linear and nonlinear fractional partial differential equations. Journal of King Saud University - Science 32:1, pages 544-549.
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Figen ÖZPINAR. (2018) Solving fractional difference equations by discrete Adomian decomposition methodAyrık Adomian ayrışım metodu ile kesirli mertebe fark denklemlerinin çözümü. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20:3, pages 15-22.
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Sami Ullah Khan & Ishtiaq Ali. (2018) Application of Legendre spectral-collocation method to delay differential and stochastic delay differential equation. AIP Advances 8:3.
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Saeid Abbasbandy. (2017) A new class of polynomial functions equipped with a parameter. Mathematical Sciences 11:2, pages 127-130.
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Necdet BİLDİK & Sinan DENİZ. (2015) MODIFIED ADOMIAN DECOMPOSITION METHOD FOR SOLVING RICCATI DIFFERENTIAL EQUATIONS. Review of the Air Force Academy 13:3, pages 21-26.
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Yalçın Öztürk & Mustafa Gülsu. (2015) Numerical solution of Riccati equation using operational matrix method with Chebyshev polynomials. Asian-European Journal of Mathematics 08:02, pages 1550020.
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Jafar Biazar & Mohsen Didgar. (2015) Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains. International Journal of Differential Equations 2015, pages 1-7.
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A. R. Vahidi, M. Didgar & R. C. Rach. (2014) An improved approximate analytic solution for Riccati equations over extended intervals. Indian Journal of Pure and Applied Mathematics 45:1, pages 27-38.
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A. R. Vahidi & M. Didgar. (2012) An improved method for determining the solution of Riccati equations. Neural Computing and Applications 23:5, pages 1229-1237.
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Berna Bülbül & Mehmet Sezer. (2013) Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method. Journal of Applied Mathematics 2013, pages 1-6.
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Şuayip Yüzbaşı. (2012) A numerical approximation based on the Bessel functions of first kind for solutions of Riccati type differential–difference equations. Computers & Mathematics with Applications 64:6, pages 1691-1705.
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Mustafa Gülsu, Yalçın Öztürk & Mehmet Sezer. (2011) On the solution of the Abel equation of the second kind by the shifted Chebyshev polynomials. Applied Mathematics and Computation 217:9, pages 4827-4833.
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Hasan Bulut & Omer Kelesoglu. (2010) Comparing numerical methods for response of beams with moving mass. Advances in Engineering Software 41:7-8, pages 976-980.
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Mehrdad Lakestani & Mehdi Dehghan. (2010) Numerical solution of Riccati equation using the cubic B-spline scaling functions and Chebyshev cardinal functions. Computer Physics Communications 181:5, pages 957-966.
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TURGUT ÖZIŞ & DENIZ AĞIRSEVEN. (2012) HE'S HOMOTOPY PERTURBATION METHOD FOR A GENERAL RICCATI EQUATION. International Journal of Modern Physics B 23:30, pages 5683-5693.
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S. Abbasbandy. (2007) A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials. Journal of Computational and Applied Mathematics 207:1, pages 59-63.
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Mustafa Gülsu & Mehmet Sezer. (2006) On the solution of the Riccati equation by the Taylor matrix method. Applied Mathematics and Computation 176:2, pages 414-421.
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Hasan Bulut, Mahmut Ergüt, Vedat Asil & Roza Horvath Bokor. (2004) Numerical solution of a viscous incompressible flow problem through an orifice by Adomian decomposition method. Applied Mathematics and Computation 153:3, pages 733-741.
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Zhou Zhengxin. (2004) The numbers of periodic solutions of the polynomial differential equation. Journal of Applied Mathematics and Computing 16:1-2, pages 265-277.
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