Name
Abstract | ||
|---|---|---|
In this study we investigate heat, wave and Poisson equations as classical models of partial differential equations (PDEs) with uncertain parameters, considering the parameters as fuzzy numbers. The fuzzy solution is built from fuzzification of the deterministic solution. The continuity of the Zadeh extension is used to obtain qualitative properties on regular @a-cuts of the fuzzy solution. We prove the stability with respect to the initial boundary data, and show that as time goes to zero, the diameter of the fuzzy solution converges to zero and, as a consequence, to the cylindrical surface determined by the curve of the degree of membership. Numerical simulations are used to obtain a graphical representation of the fuzzy solution and a defuzzification of this solution is obtained using the center of gravity method. We theoretically show that the surface obtained by defuzzification with the plane determined by fixing time is indeed the solution of the same initial boundary problem for this time-point for the heat and Poisson equations and, in a particular case, for the wave equation. The deterministic solution and the defuzzified surface intercept are numerically compared using the Euclidean distance. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.fss.2012.12.002 | Fuzzy Sets and Systems |
Keywords | Field | DocType |
wave equation,initial boundary data,fuzzy solution converges,fuzzy number,deterministic solution,defuzzified surface intercept,poisson equation,partial differential equation,initial boundary problem,cylindrical surface,fuzzy solution,partial differential equations,analysis,fuzzy numbers | Discrete mathematics,Defuzzification,Mathematical analysis,Fuzzy logic,Numerical partial differential equations,Fuzzy set,Boundary problem,Wave equation,Fuzzy number,Partial differential equation,Mathematics | Journal |
Volume | ISSN | Citations |
219, | 0165-0114 | 9 |
PageRank | References | Authors |
0.71 | 2 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ana Maria Bertone | 1 | 9 | 0.71 |
| R. Motta Jafelice | 2 | 22 | 3.51 |
| Laécio Carvalho de Barros | 3 | 36 | 3.65 |
| Rodney Carlos Bassanezi | 4 | 62 | 9.28 |