This paper aims to present the approximate solution for a thin film flow of a third grade
fluid down an inclined plane. The variation of the velocity field for different parameters has been
analyzed. The spline collocation method is used to obtain the accurate solution. The results are
shown in a tabular form as well as in a graphical manner.
Search patterns in species can give us relevant information about abundance/lack of
its food availability. This survey reviews three marked patterns: the Brownian motion, the Lévy
flight and an intermediary displacement. After defining the corresponding mathematical models
and some of its properties, we consider a general Euler scheme in which these kind of processes can
be simulated. Finally, we discuss some possible implications and future researches.
The dynamics of a fishery resource system is formulated for fish harvesting with effort
and price-sensitive demand. The model considers deterioration as damage during catchability. It is
assumed that the supply is instantaneous. The system of non-linear differential equations is
formulated and solved to determine the non-trivial equilibrium. The conditions for stability of
equilibria are worked out. The numerical data are used to support theoretical results derived.
In this paper, we investigated a numeric integration based on Magnus series expansion
namely Magnus Series Expansion Method (NMG) for nonlinear Human T-Cell Lymphotropic Virus
I (HTLV-I) infection of CD4+ T-cells model. Fourth order Magnus series expansion method (NMG4)
and explicit Runge-Kutta (RK45) are used to obtain numerical solutions of HTLV-I infection of
CD4+ T-cells model. The results obtained by NMG4 and RK45 are compared.
In this paper, on the basis of a numerical finite element method, the solution of the
Neumann problem with respect to the oscillation equation for gravity-gyroscopic waves is discussed.
The approximation with respect to spatial variables is achieved by using linear splines, and the
approximation with respect to time is achieved by using cubic Hermitean splines. It is demonstrated
that the use of such approximation with respect to time allows the quality of the solution to be
essentially improved as compared with the traditional approximation ensuring the second order
accuracy. The stability and accuracy of the method are estimated. Using the method of regularization
with spectrum shift, a new method is developed for solving the spatial operator degeneration problem
associated with the Neumann problem. The results of the numerical calculations performed provide
the possibility to make conclusions on the mode of behavior of the solution of the Neumann problem
depending on the problem variables.
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