| Paper title: |
Power Series Solution of Fuzzy Differential Equations Using Picard's Method |
| Published in: | Issue 2, (Vol. 4) / 2010 |
| Publishing date: | 2010-04-30 |
| Pages: | 72-77 |
| Author(s): | SULTANA Nasrin, KHAN A.F.M. Khodadad |
| Abstract. | In this paper we considered Picard's approximation method for finding a power series solution of a fuzzy differential equation. We showed the approximate solution tends to the exact solution both theoretically and graphically with an example. For computational and graphical purposes we used the computer algebra system Mathematica. |
| Keywords: | Fuzzy Process, Fuzzy Derivative, Fuzzy Integral, Fuzzy Differential Equation, Fuzzy Initial Value Problem, Picard’s Iterative Method. |
| References: | 1. Abbasbandy S. and Viranloo T. A., Numerical solutions of fuzzy differential equations by Taylor method, Computational Methods in Applied Mathematic 2 (2002)113-124.(c) Institute of Mathematics of the National Academy of Science of Belarus. 2. Corduneanu C., Principles of differential and integral equations, 2nd ed., Chelsea Publishing Co., Bronx, New York, 1977. MR 55 12977. 3. Done E., Ph.D., Schaum’s outline of theory and problems of Mathematica, SCHAUM’S OUTLINE SERIES, Mc Graw-Hill International Book Company, Singapore. 4. Dubios D.and Prade H.,Operations on fuzzy numbers,Inter. J. of systems sci.9(1978)613-626 5. Dubios D. and Prade H., Towards fuzzy differential calculus, Part 3: Fuzzy Sets and System 8(1982)225- 235, North-Holland. 6. Friedman M. Ma. M. and Kandel A., Numerical solutions of fuzzy differential equations, Fuzzy Sets and Systems 105(1999)133-138. 7. Goetschel Jr. Roy and Voxman William, Elementary fuzzy calculus, Fuzzy Sets and System18(1986)31- 43, North-Holland. 8. Guang-Q. Zhang, Fuzzy continuous function and its properties, Fuzzy Sets and System 16(1985)75-85, North-Holland. 9. Kaleva O. and Seikkala S., On fuzzy metric spaces. Fuzzy Sets and System 12(1984)215-229, NorthHolland. 10. Kaleva O., On the convergence of fuzzy sets, Fuzzy Sets and System 17 (1985) 53-65, North-Holland. 11. Kaleva O., Fuzzy differtial equations, Fuzzy Sets and System 24(1987)301-317, North- Holland 12. Kaleva O., The Cauchy problem for fuzzy differtial equations, Fuzzy Sets and System 35(1990)389-396, North-Holland. 13. Kaufman A. and Gupta M. M., Introduction to fuzzy arithmetic, Van Nostral Reinhold Company Inc. New York 1985. 14. Khodadad M.T. and Moghadam M.M., Linear Kstep methods for solving n-th order fuzzy differential equations, Advance in fuzzy mathematics, 1(2006)23-34,India 15.Klir J. George, Clair Ute St.and Yuan Bo., Fuzzy sets and fuzzy theory foundations and applications. International (UK) Limited, London. 16.Lipschutz S., Ph.D., Schaum’s outline of theory and problems of general Topology, Schaum’s Outline Series Mc Graw-Hill International Book Company, Singapore. 17.Puri M.L. and Ralescu, Fuzzy random variables, J. Math. Anal. And Appli.114(1886) 409-422. 18.Puri M.L. and Ralescu, Differentials for fuzzy function, J. Math. Anal and Appli 91(1983) 552- 558. 19.Rao R.M., Ordinary Differential Equations, Affiliated East-West press pvt ltd, New Delhi. 20.Seikkala S., On the initial value problem,Fuzzy Sets and System 24 (1987) 319-330, North-Holland. 21.Yeoul Jong Park and Han Hyokeun, Existance and uniqueness theorem for a solution of fuzzy differential equations, International J.Math. Sci. Vol. 22, No. 2(1999)271-279. 22.Zill G. Dennis, A first course in differential equations, 5th ed., PWS-KENT Publishing Company, Boston. |
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