An approximate solution of Riccati’s differential equation using fuzzy linguistic model

Abstract

Looking for offer, an approximate solution of the Riccati’s differential equations in this research work is based on a fuzzy linguistic model (FLM). It is shown by the FLM that it is possible to approximate continuous functions which are satisfied at the interpolation points. To obtain the function as the approximation of the solution of the RDEs, fuzzy linguistic model (FLM) was used. In numerical approaches, in order to find an approximation for a function that exists on a particular interval, just a limited number of points are utilized. However, the distinctive feature of the FLM in comparison with other approaches is that in this method all points in the arbitrary interval are used. Five examples along with their approximate solutions have been presented to show the suitability, convenience, simplicity and performance of the method. The outcomes demonstrate that the advantage of this approach compared to other methods is that there are no limiting conditions for nonlinear differential equations of order one or two with initial conditions or boundary conditions.