scholarly journals Numerical Simulation of Cyber-physical Biosensor Systems on the Basis of Lattice Difference Equations

2019 ◽  
Vol 4 (2) ◽  
pp. 91-99
Author(s):  
Vasyl Martsenyuk ◽  
◽  
Aleksandra Kłos-Witkowska ◽  
Andriy Sverstiuk ◽  
Oksana Bahrii-Zaiats
Keyword(s):  
Numerical Simulation ◽  
Difference Equations

scholarly journals An unconditionally positive and global stability preserving NSFD scheme for an epidemic model with vaccination

2014 ◽  
Vol 24 (3) ◽  
pp. 635-646 ◽  
Author(s):  
Deqiong Ding ◽  
Qiang Ma ◽  
Xiaohua Ding
Keyword(s):  
Numerical Simulation ◽  
Global Stability ◽  
Difference Equations ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Numerical Solutions ◽  
Time Step ◽  
The Stability ◽  
Nsfd Scheme ◽  
Nonstandard Finite Difference

Abstract In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that difference equations have the same dynamics as the original differential system, such as the positivity of the solutions and the stability of the equilibria, without being restricted by the time step. Our proof of global stability utilizes the method of Lyapunov functions. Numerical simulation illustrates the effectiveness of our results

scholarly journals DELAY MODELING OF MATHEMATICAL MODELS OF BIOLOGY AND IMMUNOLOGY

2021 ◽  
Vol 9 (2) ◽  
pp. 92-98
Author(s):  
T. Lunyk ◽  
I. Cherevko
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Difference Scheme ◽  
Mathematical Models ◽  
Difference Equations ◽  
Approximate Solutions ◽  
Difference Schemes ◽  
Dynamic Processes ◽  
Special Cases ◽  
Two Delays

Systems of differential-difference equations are mathematical models of many applied problems of biology, ecology, medicine, economics. The variety of mathematical models of real dynamic processes is due to the fact that their evolution does not occur instantaneously, but with some delays that have different biological interpretations. The introduction of delay allows you to build adequate mathematical models and describe new effects and phenomena in physics, ecology, immunology and other sciences. The exact solution of differential-difference equations can be found only in the simplest cases, so algorithms for finding approximate solutions of such equations are important. In this paper, a family of difference schemes is constructed for the approximate finding of solutions to initial problems with delay. Special cases are generalized Euler difference schemes. The conditions for the convergence of the generalized explicit Euler difference scheme are established. To automate the numerical simulation of systems with delays, an application program has been developed, which is used to approximate the solutions of SIR models with two delays.

Water uptake by substituted amylose tablets: experimentation and numerical simulation

2009 ◽  
Vol 00 (00) ◽  
pp. 090904073309027-8
Author(s):  
H.W. Wang ◽  
S. Kyriacos ◽  
L. Cartilier
Keyword(s):  
Numerical Simulation ◽  
Water Uptake
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