A Novel Finite-Difference Approximation to the Biharmonic Operator

A Fundamental Solution for a Biharmonic Finite-Difference Operator1

Approximation of stochastic advection diffusion equations with finite difference scheme

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

Approximation of the biharmonic problem using P1 finite elements

We study in this paper a P1 finite element approximation of the solution in H 0 (Ω) of a biharmonic problem. Since the P1 finite element method only leads to an approximate solution in H 0 (Ω), a discrete Laplace operator is used in the numerical scheme. The convergence of the method is shown, for the general case of a solution with H 0 (Ω) regularity, thanks to compactness results and to the u...

The Control-Volume Finite-Difference Approximation to the Diffusion Equation

A two-dimensional computer code for solution of the diffusion equation (Poisson equation) is described. The code is implemented in Matlab, and is intended for educational use. The partial differential equation is converted to a system of linear equations with the finite-volume method. The system is solved by a direct method, though extending the code to use iterative methods would not be diffic...

On the finite difference approximation to the convection-diffusion equation

In this paper, the system of ordinary differential equations arisen from discretizing the convection-diffusion equation with respect to the space variable to compute its approximate solution along a time level is considered. This system involves in computing ey for some vector y, where k is the time step-size and A is a large tridiagonal Toeplitz matrix. The common ways to compute an approximat...