Open AccessA modified fixed point method for biochemical transport
Author(s) -
Mohamed Ridouan Amattouch,
Hassan Belhadj
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.46947
Subject(s) - fixed point , nonlinear system , mathematics , computer science , domain (mathematical analysis) , process (computing) , work (physics) , mathematical optimization , mathematical analysis , physics , thermodynamics , quantum mechanics , operating system
This work is devoted to a modified fixed point method applied to the bio-chemical transport equation. To have a good accuracy for the solution we treat, we apply an implicit scheme to this equation and use a modified fixed point technique to linearize the problem of transport equation with a generalized nonlinear reaction and diffusion equation. Next, we apply this methods in particular to the the dynamical system of a bio-chemical process. Eventually, we accelerate these algorithms by the optimized domain decomposition methods.Several test-cases of analytical problems illustrate this approach and show the efficiency of the proposednew method.