In this paper we present a numerical method for fuzzy differential equation of fractional order under gH-fractional Caputo differentiability. The main idea of this method is to approximate the solution of fuzzy fractional differential equation (FFDE) by an implicit method as corrector and explicit method as predictor. This method is tested on numerical examples.

We present an explicit method to produce upper bounds for the dimension of the moduli spaces of complete integral Gorenstein curves with prescribed symmetric Weierstrass semigroups.

In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the sense of Caputo with order in (1, 2). The presented numerical scheme is based on the L2-1σ method in time and the Galerkin finite element method in space. The unconditional stability and ...

Jiang, H. and Y.S. Wong, A parallel alternating direction implicit preconditioning method, Journal of Computational and Applied Mathematics 36 (1991) 209-226. The alternating direction implicit (ADI) iterative method is an efficient iterative method to solve systems of linear equations due to its extremely fast convergence. The AD1 method has also been used successfully as a preconditioner in s...

The alternating direction implicit (ADI) method is an attractive option to use in avoiding the CourantFriedrichs-Lewy (CFL) condition that limits the size of the time step required by explicit finite-difference time-domain (FDTD) methods for stability. Implicit methods like Crank-Nicholson offer the same advantages as ADI methods but they do not rely on simple, one-dimensional, tridiagonal syst...

In this paper, we consider the initial boundary value problems of 1D diffusion equations. Based on a high order absolutely stable implicit scheme, we first construct two saul’yev asymmetry iterative schemes, and then present a class of parallel alternating group explicit iterative method in two cases. By use of the iterative method, the computation in the whole domain can be divided into many s...

Finite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategie...

in this article we discussed the numerical solution of Burgers’ equation using multigrid method. We used implicit method for time discritization and Crank-Nicolson scheme for space discritization for fully discrete scheme. For improvement we used Multigrid method in fully discrete solution. And also Multigrid method accelerates convergence of a basics iterative method by global correction. Nume...