scholarly journals Numerical Solution for Lotka-Volterra Model of Oscillating Chemical Reactions with Interactive Fuzzy Initial Conditions

2019 ◽  
Author(s):  
Vinícius Wasques ◽  
Estevão Esmi ◽  
Laécio C. Barros ◽  
Peter Sussner
Keyword(s):  
Numerical Solution ◽  
Chemical Reactions ◽  
Initial Conditions ◽  
Volterra Model

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

A MATHEMATICAL MODEL FOR THE REPRODUCTION DYNAMICS OF TOXOPLASMA GONDII

2015 ◽  
Vol 23 (supp01) ◽  
pp. S91-S100
Author(s):  
JOHN ALEXANDER LEÓN MARÍN ◽  
IRENE DUARTE GANDICA
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Toxoplasma Gondii ◽  
Epithelial Cells ◽  
Sexual Reproduction ◽  
Numerical Solution ◽  
Definitive Host ◽  
Initial Conditions ◽  
Felis Catus ◽  
One Dimensional

This paper presents a mathematical model describing the reproduction dynamics of the Toxoplasma gondii parasite in the definitive host Felis catus (cat). The dynamics is described by a system of partial differential equations defined in a one-dimensional region, with boundary and initial conditions. The model considers both asexual and sexual reproduction processes of the T. gondii parasite starting from the consumption of T. gondii oocysts from the environment, by the definitive host, and describing the reproduction dynamics until the cat expels infectious oocysts to the environment through its feces. The numerical solution of the system is obtained, and some simulations are made, leaving constant of transition and loss rates, since its variation does not produce significant changes in the reproduction, propagation and creation of new populations; and varying the initial consumption of oocysts from the environment by the cat. It is concluded that, either low or high, the involved populations are always reproduced; they spread by all over epithelial cells and subsequently are expelled to the environment through the cat feces. It is corroborated that the cats are potential multipliers of the oocysts and therefore, the main disseminators of the infection.

On the numerical solution of a BGK-type model for chemical reactions

2007 ◽  
Vol 26 (4) ◽  
pp. 455-472 ◽  
Author(s):  
A. Aimi ◽  
M. Diligenti ◽  
M. Groppi ◽  
C. Guardasoni
Keyword(s):  
Numerical Solution ◽  
Chemical Reactions ◽  
Type Model

scholarly journals Mathematical modeling of temperature changes impact on artificial ice islands

2021 ◽  
Vol 13 (1) ◽  
pp. 79-86
Author(s):  
Maxim V. Muratov ◽  
◽  
Vladimir A. Biryukov ◽  
Denis S. Konov ◽  
Igor B. Petrov ◽  
...  
Keyword(s):  
Numerical Solution ◽  
Stefan Problem ◽  
Initial Conditions ◽  
Economic Feasibility ◽  
The Arctic ◽  
Seasonal Temperature ◽  
Time Step ◽  
Temperature Changes ◽  
The Stability ◽  
The Impact

The article is devoted to the numerical solution of the Stefan problem for thermal effects on an artificial ice island. For modern tasks of the development of the Arctic, associated with the exploration and production of minerals, it is important to create artificial ice islands in the Arctic shelf, due to the speed of their construction, economic feasibility and other factors. The most important task for the exploitation of such islands is their stability, including against melting. This paper discusses the issue of the stability of ice islands to melting. For this, the Stefan problem on the change in the phase state of matter is formulated. An enthalpy solution method is constructed, and the applicability of this method is considered. For the numerical solution, the Peasman-Reckford scheme is used, which is unconditionally spectrally stable in the two-dimensional case, which allows to freely choose the time step. In addition, the developed approach takes into account the flow of water and the flow of melted water, which is important in the task at hand. The developed computational algorithms are parallelized for use on modern multiprocessor computing systems An approach is implemented for modeling thermal processes in the thickness of an arbitrary mass of substances, taking into account arbitrary initial conditions, environmental conditions, tidal currents of water, and solar radiation. This approach was used to calculate the temperature distribution in the thickness of the ice island, as well as to study the impact of seasonal temperature changes on the stability of the island.

scholarly journals Investigating Lotka-Volterra model using computer simulation

2020 ◽  
Vol 3 (10) ◽  
Author(s):  
F. Kunis ◽  
M. Dimitrov
Keyword(s):  
Computer Simulation ◽  
Population Dynamics ◽  
Numerical Solution ◽  
Fourth Order ◽  
Real Data ◽  
Volterra Model ◽  
Predator Prey ◽  
Prey System ◽  
Two Populations ◽  
Over Time

In this project we study the Lotka-Volterra model, also known as the model describing the population dynamics in the Predator-prey system. This model describes the interaction of the two species and also the development of their populations over time. We simulate this model using the fourth-order Runge-Kutta algorithm. This is the most widely used method for numerical solution of ordinary differential equations. Based on the obtained program, we simulated two populations and traced their behavior over time. We optimized the parameters and managed to obtain results that are very close to real data for such populations.

scholarly journals Modeling the diurnal cycle of conserved and reactive species in the convective boundary layer

2015 ◽  
Vol 8 (10) ◽  
pp. 9323-9372 ◽  
Author(s):  
D. H. Lenschow ◽  
D. Gurarie ◽  
E. G. Patton
Keyword(s):  
Boundary Layer ◽  
Planetary Boundary Layer ◽  
Chemical Reactions ◽  
Climate Models ◽  
Initial Conditions ◽  
Reactive Species ◽  
Second Order ◽  
Surface Fluxes ◽  
Great Promise ◽  
The Mean

Abstract. We have developed a one-dimensional second-order closure numerical model to study the vertical turbulent transport of trace reactive species in the convective (daytime) planetary boundary layer (CBL), which we call the Second-Order Model for Conserved and Reactive Unsteady Scalars (SOMCRUS). The temporal variation of the CBL depth is calculated using a simple mixed-layer model with a constant entrainment coefficient and zero-order discontinuity at the CBL top. We then calculate time-varying continuous profiles of mean concentrations and vertical turbulent fluxes, variances, and covariances of both conserved and chemically-reactive scalars in a diurnally-varying CBL. The set of reactive species is the O3–NO–NO2 triad. The results for both conserved and reactive species are compared with large-eddy simulations (LES) for the same free-convection case using the same boundary and initial conditions. For the conserved species, we compare three cases with different combinations of surface fluxes, and CBL and free-troposphere concentrations. We find good agreement of SOMCRUS with LES for the mean concentrations and fluxes of both conserved and reactive species except near the CBL top, where SOMCRUS predicts a somewhat shallower depth, and has sharp transitions in both the mean and turbulence variables, in contrast to more smeared out variations in the LES due to horizontal averaging. Furthermore, SOMCRUS generally underestimates the variances and species-species covariances. SOMCRUS predicts temperature-species covariances similar to LES near the surface, but much smaller magnitude peak values near the CBL top, and a change in sign of the covariances very near the CBL top, while the LES predicts a change in sign of the covariances in the lower half of the CBL. SOMCRUS is also able to estimate the intensity of segregation (the ratio of the species-species covariance to the product of their means), which can alter the rates of second-order chemical reactions; however, for the case considered here, this effect is small. The simplicity and extensibility of SOMCRUS means that it can be utilized for a broad range of turbulence mixing scenarios and sets of chemical reactions in the planetary boundary layer; it therefore holds great promise as a tool to incorporate these processes within air quality and climate models.

A method for the estimation of errors propagated in the numerical solution of a system of ordinary differential equations

1966 ◽  
Vol 25 ◽  
pp. 281-287 ◽  
Author(s):  
P. E. Zadunaisky
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Difference Method ◽  
Initial Conditions ◽  
Current Theory ◽  
Numerical Process

Let bex′=f(t,x) a system of ordinary differential equations, with initial conditionsx(a) =s, which is integrated numerically by a finite difference method of orderpand constant steph.To estimate the truncation and round-off errors accumulated during the numerical process it is established a method based on the current theory of the asymptotic behaviour (whenh→0) of errors. This method should avoid the main difficulties that arise when the results of the theory must be applied to practical cases. The method has been successfully tested and applied to estimate the errors accumulated in a numerical computation of planetary perturbations on the orbit of a comet.

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