We analyze a numerical algorithm for solving radiative transport equation with vacuum or reflection boundary condition that was proposed in [4] with angular discretization by finite element method and spatial discretization by discontinuous Galerkin or finite difference method.

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

Put options are commonly used in the stock market to protect against the decline of the price of a stock below a specified price. On the other hand, finite difference approach is a well-known and well-resulted numerical scheme for financial differential equations. As such in this work, a new spatial discretization based on finite difference semi-discretization procedure with high order of accur...

In this paper a laminar flow of water on an ice layer subjected to a slip condition is considered numerically. The paper describes a parametric mathematical model to simulate the coupled heat and mass transfer events occurring in moving boundary problems associated with a quasi steady state steady flow process. The discretization technique of the elliptic governing differential equations of mas...

An important problem that arises in different areas of science and engineering is that of computing limits of sequences of vectors fxmg, where xm 2C, and the dimension N is very large in many applications. Such vector sequences arise, for example, in the numerical solution of very large systems of linear or nonlinear equations by fixedpoint iterative methods, and limm!1xm are simply the require...

This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N) for storing the dense or even full matrices that arise from application of numerical methods and how to manage the...

A method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp-interface immersed boundary methods (IBMs) is proposed. By first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary, we adopt a cut-cell based approach to strictly enforce geometric conservati...

In this work we design and analyze a numerical method to solve efficiently two dimensional initial-boundary value reaction-diffusion problems, where the diffusion parameter can be very small in comparison with the reaction term. The method is defined by combining the Peaceman & Rachford alternating direction method to discretize in time with a finite difference scheme of HODIE type, which is de...