This paper develops the immersed interface method (IIM) due to [RJ LeVeque, Z. Li, The
immersed interface method for elliptic equations with discontinuous coefficients and singular …

A diffusion equation with nonlinear localized chemical reactions is considered in this paper.
As a result of the reactions, although the equation is parabolic, the derivatives of the solution …

Abstract An Immersed Interface Method (IIM) is developed for a reaction-diffusion problem
with discontinuous coefficients and a moving own singular source. On a regular grid using …

This paper analyzes immersed interface difference schemes for onedimensional reaction-
diffusion equations with singular own linear and nonlinear sources. Error bounds in the …

We first discuss the difficulties that arise at the construction of difference schemes on uniform
meshes for a specific elliptic interface problem. Estimates for the rate of convergence in …

Adaptive filtering is an important subfield of digital signal processing having been actively
researched for more than four decades and having important applications such as noise …

A technique combining the Rothe method with the immersed interface method (IIM) of R.
Leveque and Z. Li,[8] for numerical solution of parabolic interface problems in which the …

We present a modified iterative method for removing random-valued impulse noise. This
method has two phases. The first phase uses an adaptive center-weighted median filter to …

We study the numerical solution of a model two-dimensional problem, where the nonlinear
reaction takes place only at some interface curves, due to the present of catalyst. A finite …

Abstract In a recent paper [10], we described and analyzed a finite difference discretization
on adaptive sparse grids in three space dimensions. In this paper, we show how the discrete …