On a fractional sublinear elliptic equation with a variable coefficient

A Numerical Method for Solving Variable Coefficient Elliptic Equation with Interfaces

A Spatial Sixth Order Finite Difference Scheme for Time Fractional Sub-diffusion Equation with Variable Coefficient

In this paper, we present a finite difference scheme for a class of time fractional diffusion equation with variable coefficient, where the fractional derivative is defined by the Caputo derivative. The present algorithm is unconditionally stable, and possess spatial sixth order and temporal 2 − α order accuracy, which is an improvement of the spatial fourth order accuracy in the existing resul...

Blow-up for a reaction-diffusion equation with variable coefficient

We study the blow-up behavior for positive solutions of a reaction–diffusion equationwith nonnegative variable coefficient. When there is no stationary solution, we show that the solution blows up in finite time. Under certain conditions, we then show that any point with zero source cannot be a blow-up point. © 2012 Elsevier Ltd. All rights reserved.

Second-Order Approximation for the Space Fractional Diffusion Equation with Variable Coefficient

In this paper, we consider a type of fractional diffusion equation (FDE) with variable coefficient on a finite domain. Firstly, we utilize a second-order scheme to approximate the Riemann-Liouville fractional derivative and present the finite difference scheme. Specifically, we discuss the Crank-Nicolson scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the...

An Efficient Method for Systems of Variable Coefficient Coupled Burgers' Equation with Time-Fractional Derivative

A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered a...