[PDF] Top 20 Numerical Method For Variable-order Space Fractional Diffusion Equation and Applications

... on variable-order fractional partial differential equations is relatively new, and numerical approximation of these equations is still at an early stage of ...the variable-order ... See full document

... years, fractional differential equations (FDEs) have found applications in many problems in physics and engineering ...and numerical methods must be ...decomposition method (ADM) [5-6], ... See full document

... scenario fractional calculus plays an important role in the various fields of scientific and engineering ...problems. Fractional calculus is a field of mathematical study that grows out of the traditional ... See full document

... Using fractional order dynamics for diaphragms, bellows, and other devices that may have sprig-property yields a more accurate model for such industrial systems than the classical integer order ... See full document

... and numerical method for fractional differential equations has been devoted to FPDE’s applications, for instance, the Fourier-Laplace transform [], the Mellin transform [, ], the homotopy ... See full document

... many applications. The diffusion wave equations have been extensively used in some important physical phenomena such as percolation clusters, amorphous, colloid, glassy and porous materials through ... See full document

... Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, ... See full document

... Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, ... 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 ...obtained. Numerical tests show that the ... See full document

... diffusion equation with variable coefficients in a general bounded ...optimal order for any p in two parameter choice rules, ...the numerical examples in the one-dimensional and two-dimensional ... See full document

... tempered fractional derivatives and derived the numerical scheme for solving a tempered fractional diffusion ...a numerical scheme for one-sided space tempered fractional diffusion ... See full document

... When time dependent PDEs are solved numerically by spectral methods[1, 2], the pattern is usually the same: employ spectral treatment to space dependency and use finite difference in time or leave the time ... See full document

... Recently, numerical methods for multi-dimensional problems of fractional differential equational are ...direction method for a 2-D fractional reaction diffusion equation are ... See full document

... Fractional order differential equations are used in modeling of many phenomena in engineering, chemistry, physics, finance, and other disciplines, see [8, 14, 19] and the references ...most fractional ... See full document

... multinomial fractional ordinary differential ...three numerical solution methods to approximate the equation ...Using fractional derivative model, it will lead to a series of fractional ... See full document

... solving fractional sub-diffusion equation (1) under the conditions ...the method in Section 2 to construct unconditionally stable finite difference scheme with spatial fourth order ... See full document

... The fractional order convection diffusion equations are the generalization of the in- tegral order convection diffusion ...general fractional advection diffusion equation, it is hard to ... See full document

... multi-term variable-order fractional diffusion equation on a finite domain, which involves the Caputo variable-order time fractional derivative of order α (x, t) ∈ ... See full document

... the variable order time fractional diffusion equation is finite difference ...difference method to investigate stability and convergence of approximation for the variable ... See full document

... difference method is the most classic method for fractional differential equation ...high order accuracy schemes are seldom derived by finite difference ...extrapolation method ... See full document