A novel finite volume method for the Riesz space distributed-order advection–diffusion equation

On the split-step method for the solution of nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative

The aim of this paper is to extend the split-step idea for the solution of fractional partial differential equations. We consider the multidimensional nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative and propose an efficient numerical algorithm to obtain it's approximate solutions. To this end, we first discretize the Riesz fractional derivative then apply the Crank-...

A Novel Finite Difference Method of Order Three for the Third Order Boundary Value Problem in ODEs

In this article we have developed third order exact finite difference method for the numerical solution of third order boundary value problems. We constructed our numerical technique without change in structure of the coefficient matrix of the second-order method in cite{Pand}. We have discussed convergence of the proposed method. Numerical experiments on model test problems approves the simply...

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection-dispersion equation, which is obtained from the classical advection-diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulas for the discretisation of the fractional derivative, to numerically solve the equation on a f...

A space-time finite element method for the wave equation*

where n is a bounded open domain in R d with d ffi 1, 2 and T > 0. We have restricted our attention to a specific problem entirely to keep the presentation simple. Our results apply to considerably more general second-order hyperbolic problems. Typically an approximation to (1) is found by first discretizing in space to obtain the semidiscrete problem that consists of ordinary differential equa...

A method for solving first order fuzzy differential equation