This paper develops a two-level fourth-order scheme for solving time-fractional convection–diffusion–reaction equation with variable coefficients subjects to suitable initial and boundary conditions. The basis properties of the new approach are investigated both stability error estimates proposed numerical deeply analyzed in L∞(0,T;L2)-norm. theory indicates that method is unconditionally stabl...

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

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...

In this Part 2 of our work, we continue the discussion on time-steppers for the cable equation, modeling action potential propagation in cardiac myocyte cells. Here we report results from parallel computations. The cable equation is a diffusion-reaction PDE for transmembrane voltage, whose reaction (source) term depends on several voltage-dependent quantities (gates), each satisfying a first or...

Multidimensional integro-differential equations are obtained when the unknown function of several independent variable and/or its derivatives appear under an integral sign. When differentiation or integration operators both fractional order, equation in this case is called a multidimensional equation. Such difficult to solve analytically; therefore, as main objective paper, approximate method—w...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

Abstract: New numerical techniques are presented for the solution of a class of the variable order fractional advection-diffusion equation with a nonlinear source term on one-dimensional finite domain. Quasiwavelet and double quasi-wavelet are used for the spatial discretization. For the time stepping, Euler method is considered. We also tested the method proposed on several problems with very ...