Numerical Methods for Fuzzy Linear Partial Differential Equations under new Definition for Derivative

Document Type: Research Paper

Authors

1 Department of Mathematics, Science and Research Branch Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Nourth Tehran Branch Islamic Azad University, Tehran, Iran

Abstract

In this paper difference methods to solve "fuzzy partial differential equations" (FPDE) such as fuzzy hyperbolic and fuzzy parabolic equations are considered. The existence of the solution and stability of the method are examined in detail. Finally examples are presented to show that the Hausdorff  distance between the exact solution and approximate solution tends to zero.

Keywords


bibitem{TA} T. Allahviranloo, {it Difference methods for fuzzy partial differential equations}, Computational Methods in Appliead
Mathematics, {bf 2}textbf{(3)} (2002), 233-242.

bibitem{TAAS}T. Allahviranloo, N. Ahmadi, E. Ahmadi and K. Shamsolkotabi, {it Block jacobi two stage method for fuzzy system of
linear equations}, Appl. Math. and Com., {bf 175} (2006), 1217-1228.

bibitem{BG}B. Bede and S. Gal, {it Generalizations of the
differentiability of fuzzy number valued functions with
applications to fuzzy differential equations}, Fuzzy Sets and Systems,
{bf 151} (2005), 581-99.

bibitem{JBTHF2} J. J. Buckley and T. Feuring, {it Introduction to fuzzy
partial differential equations}, Fuzzy Sets and Systems, {bf 105} (1999), 241-248.

bibitem{BUFA} R. L. Burden and J. D. Faires, {it Numerical
analysis}, Brooks Cole, 2000.

bibitem{YH}Y. Chalco-Cano and H. Roman-Flores, {it On new solutions of
fuzzy differential equations}, Chaos Solutions and Fractals, {bf 38}textbf{(1)} (2008), 112-119.

bibitem{CHZA} S. L. Chang and L. A. Zadeh, {it On fuzzy mapping and control}, IEEE Trans Systems Man Cybernet, {bf 2} (1972), 30-34.
bibitem{DUPR} D. Dubois and H. Prade, {it Towards fuzzy differential calculus: Part 3}, Differentiation Fuzzy Sets and Systems, {bf 8} (1982), 225-233.
bibitem{GOVO} R. Goetschel and W. Voxman, {it Elementary fuzzy calculus},
Fuzzy Sets and Systems, {bf 18} (1986), 31-43.

bibitem{KA1}O. Kaleva, {it Fuzzy differential equations}, Fuzzy Sets and Systems,
{bf 24} (1987), 301-317.

bibitem{KA2}O. Kaleva, {it The cuachy problem for fuzzy differential
equations}, Fuzzy Sets and Systems, {bf 35} (1990), 389-396.

bibitem{MFAK}M. Ma, M. Friedman and A. Kandel, {it Numerical solutions
of fuzzy differential equatios}, Fuzzy Sets and Systems, {bf 105} (1999), 133-138.

bibitem{PR}M. Puri and D. Ralescu, {it Differential and fuzzy functions}, J. Math. Anal. Appl., {bf 91} (1983), 552-558.

bibitem{PURA} M. L. Puri and D. A. Ralescu, {it Differentials of fuzzy functions}, J. Math. Anal. Appl., {bf 91} (1983), 321-325.

bibitem{SE} S. Seikkala, {it On the fuzzy initial value problem}, Fuzzy Sets and Systems,
{bf 24} (1987), 319-330.