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...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

In this paper we consider a class of difference approximations to the Dirichlet problem for second-order elliptic operators with smooth coefficients. The main result is that if the order of accuracy of the approximate problem is v, and F (the right-hand side) and/ (the boundary values) both belong to Cx for X < v, then the rate of convergence is 0(hx).

in this study, we modify an iterative non-optimal without memory method, in such a way that is becomes optimal. therefore, we obtain convergence order eight with the some functional evaluations. to justify our proposed method, some numerical examples are given.

Keywords: Filter Modular space (Modular) filter convergence Rate of convergence Sampling operator Integral operator Urysohn operator Mellin convolution operator a b s t r a c t We investigate the order of approximation of a real-valued function f by means of suitable families of sampling type operators, which include both discrete and integral ones. We give a unified approach, by means of which...