scholarly journals Some Finite Difference Methods to Model Biofilm Growth and Decay: Classical and Non-Standard

Computation ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 123
Author(s):  
Yusuf Olatunji Tijani ◽  
Appanah Rao Appadu ◽  
Adebayo Abiodun Aderogba
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Biofilm Formation ◽  
Defense Mechanism ◽  
Finite Difference Methods ◽  
Difference Schemes ◽  
Diffusion Reaction ◽  
Finite Difference Schemes ◽  
Biofilm Growth ◽  
The Mathematical Model

The study of biofilm formation is undoubtedly important due to micro-organisms forming a protected mode from the host defense mechanism, which may result in alteration in the host gene transcription and growth rate. A mathematical model of the nonlinear advection–diffusion–reaction equation has been studied for biofilm formation. In this paper, we present two novel non-standard finite difference schemes to obtain an approximate solution to the mathematical model of biofilm formation. One explicit non-standard finite difference scheme is proposed for biomass density equation and one property-conserving scheme for a coupled substrate–biomass system of equations. The nonlinear term in the mathematical model has been handled efficiently. The proposed schemes maintain dynamical consistency (positivity, boundedness, merging of colonies, biofilm annihilation), which is revealed through experimental observation. In order to verify the accuracy and effectiveness of our proposed schemes, we compare our results with those obtained from standard finite difference schemes and earlier known results in the literature. The proposed schemes (NSFD1 and NSFD2) show good performance. The NSFD2 scheme reveals that the processes of biofilm formation and nutritive substrate growth are intricately linked.

A NOTE ON THE LATTICE BOLTZMANN VERSUS FINITE-DIFFERENCE METHODS FOR THE NUMERICAL SOLUTION OF THE FISHER'S EQUATION

2013 ◽  
Vol 25 (01) ◽  
pp. 1340015 ◽  
Author(s):  
SAURO SUCCI
Keyword(s):  
Finite Difference ◽  
Lattice Boltzmann ◽  
Finite Difference Methods ◽  
Difference Schemes ◽  
Diffusion Reaction ◽  
Finite Difference Schemes ◽  
Fisher’S Equation ◽  
Advection Diffusion ◽  
Fisher's Equation ◽  
Better Than

We assess the Lattice Boltzmann (LB) method versus centered finite-difference schemes for the solution of the advection–diffusion–reaction (ADR) Fisher's equation. It is found that the LB method performs significantly better than centered finite-difference schemes, a property we attribute to the near absence of dispersion errors.

scholarly journals Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 206
Author(s):  
María Consuelo Casabán ◽  
Rafael Company ◽  
Lucas Jódar
Keyword(s):  
Stochastic Process ◽  
Finite Difference ◽  
Coming Out ◽  
Finite Difference Methods ◽  
Diffusion Reaction ◽  
Finite Difference Schemes ◽  
Finite Degree ◽  
Mean Square Stability ◽  
Reaction Models ◽  
Difference Methods

This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

Finite difference methods for 2D shallow water equations with dispersion

2019 ◽  
Vol 34 (2) ◽  
pp. 105-117 ◽  
Author(s):  
Gayaz S. Khakimzyanov ◽  
Zinaida I. Fedotova ◽  
Oleg I. Gusev ◽  
Nina Yu. Shokina
Keyword(s):  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Difference Methods ◽  
Original System ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Elliptic Type ◽  
Two Dimensional ◽  
Nonlinear Hyperbolic System

Abstract Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively different in the cases the dispersion is taken into account, or not. The difference in the behavior of phase errors in one- and two-dimensional cases is pointed out. Special attention is paid to the numerical algorithm based on the splitting of the original system of equations into a nonlinear hyperbolic system and a scalar linear equation of elliptic type.

scholarly journals ON MATHEMATICAL MODELLING OF METALS DISTRIBUTION IN PEAT LAYERS

2014 ◽  
Vol 19 (4) ◽  
pp. 568-588
Author(s):  
Ilmars Kangro ◽  
Harijs Kalis ◽  
Aigars Gedroics ◽  
Erika Teirumnieka ◽  
Edmunds Teirumnieks
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Finite Difference ◽  
Diffusion Coefficients ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Circulant Matrix ◽  
Elliptic Type ◽  
Difference Methods ◽  
The Mathematical Model

In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in multilayered domain. We consider the metals Fe and Ca concentration in the layered peat blocks. Using experimental data the mathematical model for calculation of concentration of metals in different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations (PDEs) of second order with piece-wise diffusion coefficients in the layered domain. We develop here a finite-difference method for solving of a problem of one, two and three peat blocks with periodical boundary condition in x direction. This procedure allows to reduce the 3-D problem to a system of 2-D problems by using circulant matrix.

Characteristics of finite difference methods for dispersive shallow water equations

2016 ◽  
Vol 31 (3) ◽  
Author(s):  
Zinaida I. Fedotova ◽  
Gayaz S. Khakimzyanov
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Finite Difference Methods ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Hydrodynamic Equations ◽  
Difference Methods

AbstractThe paper contains a description of the most important properties of numerical methods for solving nonlinear dispersive hydrodynamic equations and their distinctions from similar properties of finite difference schemes approximating classic dispersion-free shallow water equations.

scholarly journals Finite Difference Methods for Weather Prediction in Abuja, Nigeria

2020 ◽  
pp. 915-931
Author(s):  
Jacob Emmanuel ◽  
Ogunfiditimi F.O. ◽  
Victor Alexander Okhuese ◽  
Odeyemi J. K
Keyword(s):  
Finite Difference ◽  
Weather Prediction ◽  
Finite Difference Methods ◽  
Weather Forecast ◽  
Difference Schemes ◽  
Weather Data ◽  
Finite Difference Schemes ◽  
Numerical Weather ◽  
Difference Methods ◽  
The Finite Difference Method

In this research, we have been able to simulate some finite difference schemes to predict weather trends of Abuja Station, Nigeria. By analyzing the results from these schemes, it has shown that the best scheme in the finite difference method that gives a close accurate weather forecast is the trapezoidal scheme hence we use it to simulate numerical weather data obtained from Federal Airports Authority of Nigeria (FAAN), Abuja and corresponding numerical weather data obtained by the compatible finite difference schemes, using MATLAB (R2012a) software to obtain future numerical weather trends.

scholarly journals THE MATHEMATICAL SIMULATION OF THE LIQUID TRANSPORT IN A MULTILAYERED NONWOVEN

1997 ◽  
Vol 2 (1) ◽  
pp. 9-34 ◽  
Author(s):  
Raimondas Čiegis ◽  
Aivars Zemitis
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Parallel Algorithms ◽  
Mathematical Simulation ◽  
Numerical Experiments ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Differential Problem ◽  
Liquid Transport ◽  
Optimization Task

In this report we treat an optimization task, which should make the choice of nonwovens for making diapers faster. A mathematical model for the liquid transport in nonwoven is developed. Finite‐difference schemes are proposed for numerical solving of the differential problem. Parallel algorithms are considered and results of numerical experiments are given.

scholarly journals The Mathematical Modeling of Metals Mass Transfer in Three Layer Peat Blocks

2015 ◽  
Vol 1 ◽  
pp. 87
Author(s):  
Ērika Teirumnieka ◽  
Ilmārs Kangro ◽  
Edmunds Teirumnieks ◽  
Harijs Kalis
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Mathematical Models ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Difference Methods ◽  
The Mathematical Model

The mathematical model for calculation of concentration of metals for 3 layers peat blocks is developed due to solving the 3-D boundary-value problem in multilayered domain-averaging and finite difference methods are considered. As an example, mathematical models for calculation of Fe and Ca concentrations have been analyzed.

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