scholarly journals Numerical algorithms for solving the optimal control problem of simple bioreactors

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Raimondas Čiegis ◽  
Remigijus Čiegis
Keyword(s):  
Nonlinear Diffusion ◽  
Finite Difference Methods ◽  
Numerical Algorithms ◽  
External Boundary ◽  
Enzymatic Conversion ◽  
Control Loop ◽  
Potential Accuracy ◽  
Difference Methods ◽  
Diffusion Convection ◽  
Reaction Equations

The modified nonlocal feedback controller is used to control the production of drugs in a simple bioreactor. This bioreactor is based on the enzymatic conversion of substrate into the required product. The dynamics of this device is described by a system of two nonstationary nonlinear diffusion–convection–reaction equations. The analysis of the influence of the convection transport is one the aims of this paper. The control loop is defined using the relation, which shows how the amount of the drug produced in the bioreactor and delivered into a human body depends on the substrate concentration specified on the external boundary of the bioreactor. The system of PDEs is solved by using the finite volume and finite difference methods, the control loop parameters are defined from the analysis of stationary linearized equations. The second aim of this paper is to solve the inverse problem and to determine optimal boundary conditions. These results enable us to estimate the potential accuracy of the proposed devices.  

TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DIFFUSION–CONVECTION–REACTION MODELS

2013 ◽  
Vol 23 (10) ◽  
pp. 1350168
Author(s):  
JIBIN LI ◽  
JIANPING SHI
Keyword(s):  
Traveling Wave ◽  
Nonlinear Diffusion ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Heteroclinic Orbits ◽  
Wave System ◽  
Wave Solutions ◽  
Kink Wave ◽  
Diffusion Convection ◽  
Reaction Equations

For a class of nonlinear diffusion–convection–reaction equations, corresponding to two families of heteroclinic orbits connecting two nodes of the traveling wave system, the existence of uncountably infinite many global monotonic and nonmonotonic wavefront solutions is discussed. By using the method of planar dynamical systems, the dynamical behavior of the corresponding traveling wave system is studied. Under some parametric conditions, exact explicit parametric representations of the monotonic and nonmonotonic kink wave solutions are given.

scholarly journals MODIFIED FINITE-DIFFERENCE SCHEME FOR SOLVING ONE CLASS OF CONVECTION-REACTION-DIFFUSION PROBLEMS

2021 ◽  
pp. 7-14
Author(s):  
Anna Vladimirovna Pavelchuk ◽  
◽  
Anna Gennadievna Maslovskaya ◽  
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Reaction Diffusion ◽  
Time Dependent ◽  
Computational Scheme ◽  
Multidimensional Equation ◽  
Difference Methods ◽  
Alternating Directions Method ◽  
Diffusion Convection ◽  
Diffusion Problems

The paper reviews approaches to the construction of finite-difference methods for solving time-dependent diffusion equations and transport equations. A modified computational scheme for solving a semilinear multidimensional equation of the «reaction – diffusion – convection» type is presented. The hybrid computational scheme is based on the alternating directions method and the Robert-Weiss scheme.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

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.

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