Combined Optimized Domain Decomposition Method and a Modified Fixed Point Method for Non Linear Diffusion Equation

A modified fixed point method for biochemical transport

“…) is equivalent to the global minimization of the Energy E on the space H with some constraints. We can prove that E is a K contraction on V for a small number M (see [1], [2] for prove and explanation in the case of nonlinear diffusion). This method is local and could diverge for an initial sequence departure is u 0 = h 0 .…”

“…As a solution to this problem we make some modifications to the equation to have successive sequences that are not distant from the initial value u 0 = h 0 . As in [2] where, we proposed a modified fixed point to a just a semi linear equation, and in [1] where, we applied a modified fixed point to a nonlinear equation, we generalize this method to our equation by mean of solving the following iterative equations:…”

“…Also, the use of explicit scheme to solve these equations is not accurate, stable and efficient in general . So In order to make ours bio-chemicals simulations fast, stable and efficient, we apply in this paper, the modified fixed point (we propose in [1], [2], [4]) to solve problem (1.1) type.…”