Numerical Approximate Solution of Fuzzy Volterra Nonlinear Integro-Differential Equation

Abstract

In this work, approximate solutions to fuzzy integro-differential equations refer to numerical methods or techniques used to obtain approximate solutions to differential equations involving fuzzy sets and integro-differential operators. Fuzzy integro-differential equations have recently increased as a model for many problems in the fields of science and technology, and so we propose efficient approximate methods to solve nonlinear fuzzy integro-differential equations. Therefore, nonlinear fuzzy integro-differential equations are usually complex to solve analytically, and exact solutions are scarce. We combined two numerical methods to obtain an approximate solution to the nonlinear fuzzy Volterra integro-differential equation of the first and second order. Specifically, we combined the fuzzy Euler predictor-corrector and fuzzy Taylor expansion with fuzzy Newton-Cotes integration, respectively. Finally, the applicability and validity of the numerical approaches are demonstrated, and the findings show that the proposed methods' convergence and accuracy agree closely with the exact solution. These findings are shown in tables and graphical figures.