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Runge-Kutta methods for fuzzy differential equations. (English) Zbl 1161.65058
Summary: Fuzzy differential equations (FDEs) generalize the concept of crisp initial value problems. In this article, we deal with the numerical solution of FDEs. The notion of convergence of a numerical method is defined and a category of problems which is more general than the one already found in the numerical analysis literature is solved. Efficient s-stage Runge-Kutta methods are used for the numerical solution of these problems and the convergence of the methods is proved. Several examples comparing these methods with the previously developed Euler method are displayed.
65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
26E50Fuzzy real analysis
65L20Stability and convergence of numerical methods for ODE
[1]Abbasbandy, S.; Viranloo, T. Allah: Numerical solution of fuzzy differential equation by Runge – Kutta method, Nonlinear studies 11, No. 1, 117-129 (2004) · Zbl 1056.65069
[2]Buckley, J. J.; Feuring, T.: Fuzzy differential equations, Fuzzy sets and systems 110, 43-54 (2000) · Zbl 0947.34049 · doi:10.1016/S0165-0114(98)00141-9
[3]Butcher, J. C.: The numerical analysis of ordinary differential equations, (1987) · Zbl 0616.65072
[4]Dubois, D.; Prade, H.: Towards fuzzy differential calculus part 3: differentiation, Fuzzy sets and systems 8, 225-233 (1982) · Zbl 0499.28009 · doi:10.1016/S0165-0114(82)80001-8
[5]Goetschel, R.; Voxman, W.: Elementary fuzzy calculus, Fuzzy sets and systems 18, 31-43 (1986) · Zbl 0626.26014 · doi:10.1016/0165-0114(86)90026-6
[6]Hairer, E.; Norsett, S. P.; Wanner, G.: Solving ordinary differential equations I, (1987)
[7]Kaleva, O.: Fuzzy differential equations, Fuzzy sets and systems 24, 301-317 (1987) · Zbl 0646.34019 · doi:10.1016/0165-0114(87)90029-7
[8]Kolmogorov, A. N.; Fomin, S. V.: Introductory real analysis, (1970) · Zbl 0213.07305
[9]Lambert, J. D.: Numerical methods for ordinary differential systems, (1990)
[10]Ma, M.; Friedman, M.; Kandel, A.: Numerical solutions of fuzzy differential equations, Fuzzy sets and systems 105, 133-138 (1999) · Zbl 0939.65086 · doi:10.1016/S0165-0114(97)00233-9
[11]Puri, M. L.; Ralescu, D. A.: Differentials of fuzzy functions, Journal of mathematical analysis and applications 91, 552-558 (1983) · Zbl 0528.54009 · doi:10.1016/0022-247X(83)90169-5
[12]Seikkala, S.: On the fuzzy initial value problem, Fuzzy sets and systems 24, 319-330 (1987) · Zbl 0643.34005 · doi:10.1016/0165-0114(87)90030-3