[PDF] Top 20 Pseudo Spectral Method for Space Fractional Diffusion Equation

... Chebyshev spectral collocation method (often called pseudo-spectral) is used in this ...spatial fractional de- rivatives are easily computed and a system of ordinary differential ... See full document

... the fractional derivative in describing the memory and genetic of material has a natural ...Thus fractional derivatives are applied to many science fields, especially in the analytical [–] and numerical ... See full document

... symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential ...the diffusion equation, a fully discrete ... See full document

... for space fractional order differential equations with inhomogeneous boundary ...for fractional diffusion-wave ...difference-spectral method for solving space ... See full document

... multinomial fractional ordinary differential ...the equation solution. Using fractional derivative model, it will lead to a series of fractional differential equations in most ...for ... See full document

... with fractional orders 1 <   2 and 1 <   2 , where the diffusion coefficients d x y  , 0   and e x y  , 0   ...this fractional diffusion equation has a unique and ... See full document

... Fourier method is used to identify the unknown source term depending only on the spatial variable for a Riesz-Feller space-fractional diffusion ... See full document

... time fractional advection diffusion equations was given in ...the space-time-fractional ad- vection diffusion equation were discussed in ...time fractional advection diffusion ... See full document

... The fractional diffusion-wave equation is a mathematical model of some important physical phenomena ...the equation with constant coefficients in the whole space and half-space by Green ... See full document

... Fokker-Planck equation into a system of ordinary differential equations suggested in( [15], [16]) ....The space fractional diffusion equations are solved numerically ...collocation ... See full document

... (EFK) equation plays an important role. In this paper, a Fourier pseudo-spectral method for solving the EFK equation in two space dimensions is ...Crank-Nicolson method is ... See full document

... time-space fractional diffusion ...the space domain, we use a set of normalized Bernstein polynomials and for the time domain, which is a semi-infinite domain, we offer an algebraic map to make the ... See full document

... β-order fractional derivative using the Gr¨unwald finite difference formula at all time ...difference equation regardless of whatever result in finite difference method is an explicit or an implicit ... See full document

... analysis method [1], homotopy perturbation method [12, 46], Adomian decomposition method [11, 31], multi-step differential transform method [7, 8, 13], Kansa method [5], finite ... See full document

... been successfully applied to find the solution of space fractional diffusion equation. All cases show that the results of the ADM method are very good and the ob- tained solutions are ... See full document

... Lagrange’s spectral method for 2D space fractional diffusion equation are ...proposed method and to compare the performance of four types of ... See full document

... numerical method is considered for solving the fractional wave equation ...The fractional derivative is described in the Caputo sense. The method is based on La- guerre ...difference ... See full document

... ing q () = q ∗ . This represents a strong perturbation in the initial guess. We now fix M = N = , α = .. In Figure , we plot the convergence history of the gradient of the objective function as a function of the ... See full document

... Marchaud fractional integration and differentiation of the case of variable order, and then showed some properties and an inversion ...the fractional derivative as the starting point to suggest a novel ... See full document

... m = with the final time T = 2 are given. Also, in Figure 1 and Figure 2, comparison between the exact solution and the approximate solution at T = 0.5 with time step τ = 0.0025 , m = 3 and m = 5 , are presented, ... See full document