Method of directly defining the inverse mapping for nonlinear fuzzy heat-like partial differential equations

Abstract

Natural phenomena or physical systems can be described using Partial Differential Equations (PDEs), such as wave equations, heat equations, Poisson’s equation, and so on. Consequently, investigations of PDEs have become one of the key areas of modern mathematical analyses, attracting a lot of attention. Many authors have recently expressed an interest in researching the theoretical framework of fuzzy Initial Value Problems (IVPs). The Method of Directly Defining the inverse Mapping (MDDiM) was effectively employed in this research to obtain the second-order approximate fuzzy solution of heatlike equations in one and two dimensions, and the results were compared with exact solutions. In each illustrated example, all the results achieved using Maple 16 were graphically depicted. This is the first time MDDiM was utilized to solve nonlinear Fuzzy Partial Differential Equations (FPDEs).