Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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SOLUTION OF RICCATI TYPES MATRIX DIFFERENTIAL EQUATIONS USING MATRIX DIFFERENTIAL TRANSFORM METHOD

  • Abazari, Reza (Department of Mathematics, University of Mohaghegh Ardabili)
  • 발행 : 2009.09.30
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초록

In this work, we successfully extended dimensional differential transform method (DTM), by presenting and proving some new theorems, to solve the non-linear matrix differential Riccati equations(first and second kind of Riccati matrix differential equations). This technique provides a sequence of matrix functions which converges to the exact solution of the problem. Examples show that the method is effective.

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참고문헌

  1. H. Kwakernaak and R. Sivan,Linear Optimal Control Systems, Wiley Interscience, NewYork, 1972.
  2. L. Dieci,Numerical integration of the differential Riccati equation and some related issues, SIAM J. Numer. Anal.29(3)(1992), 781-815. https://doi.org/10.1137/0729049
  3. L. Dieci, M. R. Osborne, and R. D. Russell,A Riccati transformation method for solving linear BVPs. I: Theoretical aspects, SIAM Journal on Numerical Analysis, 25 (1988), 1055-1073. https://doi.org/10.1137/0725061
  4. C.S. Kenney, R.B. Leipnik,Numerical integration of the differential matrix Riccati equation, IEEE Trans. Automat. Contr. AC-30 (1985), 962-970.
  5. Chiu H. Choi,A survey of numerical methods for solving matrix Riccati differential equations, Southeastcon90 Proc. (1990), 696-700.
  6. C. Choi Chiu, J. Laub Alan,Efficient matrix-valued algorithms for solving stiff Riccati differential equations, IEEE Trans. Automat. Contr.35 (7) (1990), 770-776. https://doi.org/10.1109/9.57015
  7. A. Borhanifar, Reza Abazari,Numerical Solution of Second-Order Matrix Differential Models Using Cubic Matrix Splines, Applied Mathematical Sciences 59 (2007), 2927-2937.
  8. M.M. Tunga, E. Defez, J. Sastre,Numerical solutions of second-order matrix models using cubic-matrix splines, Comput. Math. Appl. http://doi:10.1016/j.camwa.2008.05.022.
  9. J.K. Zhou,Differential Transformation and its Application for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
  10. Fatma Ayaz,Solutions of the system of differential equations by differential transform method, Appl. Math. Comput. 147 (2004), 547-567. https://doi.org/10.1016/S0096-3003(02)00794-4
  11. F. Ayaz,Application of differential transform method to differential-algebraic equations, Appl. Math. Comput. 152 (2004), 649-657. https://doi.org/10.1016/S0096-3003(03)00581-2
  12. Figen Kangalgil, Fatma Ayaz,Solitary wave solutions for the KdV and mKdV equations by differential transform method, Chaos, Solitons & Fractals, 41 (2009), 464-472. https://doi.org/10.1016/j.chaos.2008.02.009
  13. Momani S, Odibat Z, Hashim I,Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods, Topological method in Nonlinear Analysis, 31 (2008), 211-226.
  14. Y. Keskin, A. Kurnaz, M.E. Kiris, G. Oturanc,Approximate solutions of generalized pantograph equations by the differential transform method, Int. J. Nonlinear Sci. 8 (2007), 159-164.
  15. A. Arikoglu, I. Ozkol,Solution of boundary value problems for integro-differential equations by using differential transform method, Appl. Math. Comput. 168 (2005), 1145-1158. https://doi.org/10.1016/j.amc.2004.10.009