In this paper, a general and systematic scheme is formulated for finding approximate solutions of two-way diffusion equations. This expansion scheme is valid for arbitrary mean-free path and can be carried out to any desired accuracy. Its potential is demonstrated by constructing approximate solutions for two problems concerning the kinetics of an electron beam, and the accuracy is found to be ...

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. In case of advection-diffusion equations, so far there have been not found stable schemes with positive difference coefficients in a family of numerical sch...

The numerical solution of a singularly perturbed semilinear reaction-diffusion two-point boundary value problem is addressed. The method considered is adaptive movement of a fixed number (N +1) of mesh points by equidistribution of a monitor function that uses discrete second-order derivatives. We extend the analysis by Kopteva & Stynes (2001) to a new equation and a more intricate monitor func...

in this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by boundary elements. the integrals in boundary integrals equations are inherently singular. for example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

By using the finite element $p$-Version in convection-diffusion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the finite element $p$-Version is augmentation degrees of freedom. Based on the fact that the finite element and the meshless methods have similar concept, it is obvious that many ideas in the finite element can be easily used in the meshl...

In this paper, the role of molecular diffusion in mobilization of waterflood residual oil is examined. A moving mesh method is applied to solve the moving interface problem of residual oil blobs swelling by Co2 diffusion through a blocking water phase. The results of this modeling are compared with experimental results of a 2D glass micromodel experiment. Although, the solution method is applie...

We present an hp-adaptive virtual element method (VEM) based on the hypercircle of Prager and Synge for approximation solutions to diffusion problems. introduce a reliable efficient posteriori error estimator, which is computed by solving auxiliary global mixed problem. show that VEM satisfies discrete inf-sup condition with constant independent discretization parameters. Furthermore, we constr...

Abstract— There are several works dedicated to the investigation of Volterra integro-differential equations. In addition, there are theoretical and practical representations of stable methods that have a high order of accuracy and extended stability regions; these representations were constructed using the minimum values of arithmetic operations. Here, hybrid methods are proposed for the constr...