Comparative analysis of two ideologically distinct approaches in the theory of fuzzy di"erential equations is given. Domains of applications, advantages and shortcomings of those approaches are described. New de2nitions of solutions to fuzzy di"erential equations are proposed. c © 2002 Elsevier Science B.V. All rights reserved.

Rapid thermal processing (RTP) is a new technique for performing various wafer fabrication operations such as annealing, oxidation and chemical vapor deposition in a single chamber. The success of the RTP depends on the precise control of wafer temperature by adjusting wall heat ̄ux. In the present investigation, an ecient recursive method is developed to solve the inverse heat transfer proble...

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

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For the approximate representation of large data sets over a parameter domain in IR2, many geological and other applications require the construction of surfaces which have minimal energy, i.e., minimal curvature. One way to achieve this is by solving a fourth order elliptic partial di erential equation. Its discretization by a di erence scheme makes it particularly easy to incorporate (appropr...

This paper presents a new method for solving di erential algebraic equation systems using a mixed symbolic and numeric approach Discretization formu lae representing the numerical integration algorithm are symbolically inserted into the di erential algebraic equation model The symbolic formulae manipulation algorithm of the model translator treats these additio nal equations in the same way as ...

Abstract. We present a new tunably-accurate Laguerre Petrov-Galerkin spectral method for solving linear multi-term fractional initial value problems with derivative orders at most one and constant coe cients on the half line. Our method results in a matrix equation of special structure which can be solved in O(N logN) operations. We also take advantage of recurrence relations for the generalize...

A neural network based optimal control synthesis approach is presented for systems modeled by partial di!erential equations. The problem is formulated via discrete dynamic programming and the necessary conditions of optimality are derived. For synthesis of the controller, we propose two sets of neural networks: the set of action networks captures the mapping between the state and control, while...

1. Preliminaries. Multigrid methods originated earlier this century, in the personnel computing era. Someone who needed to compute an approximation to the solution of a partial di erential equation during that era would ll a room with people. After using very simple mechanical calculators to compute parts of the approximation, these people would pass their parts to the other people in the room ...