Fuzzy Numerical Schemes for Hyperbolic Differential Equations

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 setup, 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.