Proceedings of the Korean Society of Computational and Applied Mathematics Conference (한국전산응용수학회:학술대회논문집)
- 2003.09a
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- Pages.4.2-4
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- 2003
Graphic Representation of Solutions of Partial Differential Equations Using their Corresponding Fuzzy Systems
Abstract
In this paper, we describe how to approximate the solutions of partial differential equations by bicubic spline functions whose interpolation errors at non-grid points are smaller in general than those by linear interpolations of the original solution at grid points. We show that the bicubic spline function can be represented exactly or approximately by a fuzzy system, and that the resulting fuzzy rule table shows the contours of the solution function. Thus, the fuzzy rule table is identified as a digital image and the contours in the rule table provide approximate contours of the solution of partial differential equations. Several illustrative examples are included.
Keywords