Stability of finite difference schemes for nonlinear complex reaction–diffusion processes

Stability of Finite Difference Schemes for Complex Diffusion Processes

Abstract: Complex diffusion is a common and broadly used denoising procedure in image processing. The method is based on an explicit finite difference scheme applied to a diffusion equation with a proper complex diffusion parameter in order to preserve edges and the main features of the image, while eliminating noise. In this paper we present a rigorous proof for the stability condition of comp...

Finite Difference Schemes for Nonlinear Complex Reaction-diffusion Processes: Stability Analysis

In this paper we establish the stability condition of a general class of finite difference schemes applied to nonlinear complex reaction-diffusion equations. We consider the numerical solution of both implicit and semi-implicit discretizations. To illustrate the theoretical results we present some numerical examples computed with a semi-implicit scheme applied to a nonlinear equation.

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

Convergence of Finite Difference Schemes for Nonlinear Complex Reaction-Diffusion Processes

Lie Group Stability of Finite Difference Schemes

Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference approximation, and leading to inaccurate numerical results. This paper proposes a method that enables us to build a scheme that preserves some of those symmetries.