Convergence, Consistency and Stability in Fuzzy Differential Equations

convergence, consistency and stability in fuzzy differential equations

in this paper, we consider first-order fuzzy differential equations with initial value conditions. the convergence, consistency and stability of difference method for approximating the solution of fuzzy differential equations involving generalized h-differentiability, are studied. then the local truncation error is defined and sufficient conditions for convergence, consistency and stability of ...

Convergence, Stability, and Consistency of Finite Difference Schemes in the Solution of Partial Differential Equations

A finite difference scheme is produced when the partial derivatives in the partial differential equation(s) governing a physical phenomenon are replaced by a finite difference approximation. The result is a single algebraic equation or a system of algebraic equations which, when solved, provide an approximation to the solution of the original partial differential equation at selected points of ...

Solution of fuzzy differential equations

Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎The hybrid differential equations have a wide range of applications in science and engineering‎. ‎The hybrid systems are devoted to modeling‎, ‎design‎, ‎and validation of interactive systems of computer programs and continuous systems‎. ‎Hybrid fuzzy differential equations (HFDEs) is considered by ...

Fuzzy Local Fractional Differential Equations

Stability, consistency, and convergence of numerical discretizations

A problem in differential equations can rarely be solved analytically, and so often is discretized, resulting in a discrete problem which can be solved in a finite sequence of algebraic operations, efficiently implementable on a computer. The error in a discretization is the difference between the solution of the original problem and the solution of the discrete problem, which must be defined s...

Cascade of Fractional Differential Equations and Generalized Mittag-Leffler Stability

This paper address a new vision for the generalized Mittag-Leffler stability of the fractional differential equations. We mainly focus on a new method, consisting of decomposing a given fractional differential equation into a cascade of many sub-fractional differential equations. And we propose a procedure for analyzing the generalized Mittag-Leffler stability for the given fractional different...