Fuzzy general linear methods

TL;DR

This paper develops a comprehensive framework called Fuzzy General Linear Methods (FGLM) for solving fuzzy differential equations, extending classical methods to handle fuzziness with proven stability and accuracy.

Contribution

It introduces the FGLM framework based on Adams schemes for fuzzy differential equations, addressing stability, consistency, and convergence under generalized differentiability.

Findings

Numerical results demonstrate the scheme's efficiency.

The method achieves high order of accuracy.

Stability and convergence are theoretically established.

Abstract

This paper concerns with the developing the most general schemes so-called Fuzzy General Linear Methods (FGLM) for solving fuzzy differential equations. The general linear methods (GLM) for ordinary differential equations are the middle state of two extreme extensions (linear multistep and Runge-Kutta methods) of the one step Euler method. In this paper we develop the FGLM framework of the Adams schemes for solving fuzzy differential equations under the strongly generalized differentiability. The stability, consistency and convergent results will be addressed. The numerical results and the order of accuracy is illustrated to show the efficiency and accuracy of the novel scheme.