Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator
نویسندگان
چکیده
In this paper, we present a numerical solution to an ordinary differential equation of a fractional order in one-dimensional space. The solution to this equation can describe a steady state of the process of anomalous diffusion. The process arises from interactions within complex and non-homogeneous background. We present a numerical method which is based on the finite differences method. We consider a boundary value problem (Dirichlet conditions) for an equation with the Riesz-Feller fractional derivative. In the final part of this paper, same simulation results are shown. We present an example of non-linear temperature profiles in nanotubes which can be approximated by a solution to the fractional differential equation.
منابع مشابه
Numerical Solutions of a Boundary Value Problem for the Anomalous Diffusion Equation with the Riesz Fractional Derivative
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the complex and non-homogeneous background. We presented a numerical method which bases on the finite differences method. We considered pure initial and boundaryini...
متن کاملNumerical simulations for a variable order fractional Schnakenberg model
This paper is concerned with the numerical solutions of a variable-order space-time fractional reaction-diffusion model. The space-time fractional derivative is considered in the sense of Riesz-Feller, the system is defined by replacing the second order space derivatives with the variable Riesz-Feller derivatives. The problem is solved by an explicit finite difference method. Finally, simulatio...
متن کاملNumerical treatment of an initial-boundary value problem for fractional partial differential equations
This paper deals with numerical solutions to a partial differential equation of fractional order. Generally this type of equation describes a transition from anomalous diffusion to transport processes. From a phenomenological point of view, the equation includes at least two fractional derivatives: spatial and temporal. In this paper we proposed a new numerical scheme for the spatial derivative...
متن کاملOn 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-...
متن کامل