TY - JOUR
ID - 10908
TI - Solving free boundary problem for an initial cell layer in multispecies biofilm formation by Newton-Raphson method
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Ivaz, Karim
AU - Asadpour Fazlallahi, Mohammad
AD - Faculty of Mathematical sciences,
University of Tabriz, Tabriz, Iran.
Y1 - 2021
PY - 2021
VL - 9
IS - 3
SP - 899
EP - 907
KW - biofilm
KW - Newton-Raphson method
KW - Free boundary problem
KW - nonlinear system of Volterra integral equations
DO - 10.22034/cmde.2020.39940.1746
N2 - The initial attached cell layer in multispecies biofilm growth is studied in this paper. The corresponding mathematical model leads to discuss a free boundary problem for a system of nonlinear hyperbolic partial differential equations, where the initial biofilm thickness is equal to zero. No assumptions on initial conditions for biomass concentrations and biofilm thickness are required. The data that the problem needs are the concentration of biomass in the bulk liquid and biomass flux from the bulk liquid. The differential equations are converted into an equivalent system of Volterra integral equations. We use Newton-Raphson method to solve the nonlinear system of Volterra integral equations (SVIEs) of the second kind. This method converts the nonlinear system of integral equations into a linear integral equation at each step.
UR - https://cmde.tabrizu.ac.ir/article_10908.html
L1 - https://cmde.tabrizu.ac.ir/article_10908_082747e2679c9a440406ec4a05720457.pdf
ER -