The numerical solution of hyperbolic partial differential equations (PDEs) is an important topic in natural sciences and engineering. One of the main difficulties in the task stems from the need to employ several basic types of approximations that are blended in a nonlinear way. In this paper we show that fuzzy logic can be used to construct novel nonlinear blending functions. After introducing the set-up, we show by numerical experiments that the fuzzy-based schemes outperform methods based on conventional blending functions. To the knowledge of the authors, this paper represents the first work where fuzzy logic is applied for the construction of simulation schemes for PDEs. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Breuss, M., & Dietrich, D. (2009). Fuzzy numerical schemes for hyperbolic differential equations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5803 LNAI, pp. 419–426). https://doi.org/10.1007/978-3-642-04617-9_53
Mendeley helps you to discover research relevant for your work.