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1
Content available Computational scheme for a differential difference equation with a large delay in convection term
Erla Srinivas, Kolloju Phaneendra
International Journal of Applied Mechanics and Engineering
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2023
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Vol. 28, no. 2
34--48
EN
A computational scheme for the solution of layer behaviour differential equation involving a large delay in the derivative term is devised using numerical integration. If the delay is greater than the perturbation parameter, the layer structure of the solution is no longer preserved, and the solution oscillates. A numerical method is devised with the support of a specific kind of mesh in order to reduce the error and regulate the layered structure of the solution with a fitting parameter. The scheme is discussed for convergence. The maximum errors in the solution are tabulated and compared to other methods in the literature to verify the accuracy of the numerical method. Using this specific kind of mesh with and without the fitting parameter, we also studied the layer and oscillatory behavior of the solution with a large delay.
2
Content available Stochastic model of drug concentration level during IV-administration
Dzhalladova Irada, Růžičková Miroslava
Opuscula Mathematica
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2022
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Vol. 42, no. 6
833--847
EN
A stochastic model describing the concentration of the drug in the body during its IV-administration is discussed. The paper compares a deterministic model created with certain simplifications with the stochastic model. Fluctuating and irregular patterns of plasma concentrations of some drugs observed during intravenous infusion are explained. An illustrative example is given with certain values of drug infusion rate and drug elimination rate.
3
Content available On existence and global attractivity of periodic solutions of nonlinear delay differential equations
Qian Chuanxi, Smith Justin
Opuscula Mathematica
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2019
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Vol. 39, no. 6
839--862
EN
onsider the delay differential equation with a forcing term [formula] (*) where ƒ (t, x) : [0,) x [0, ∞) —> R, g(t, x) : [0, ∞) x [0, ∞) —> [0, ∞) are continuous functions and w-periodic in t, r(t) : [0, ∞) —> R is a continuous function and r ∈ (0, ∞) is a positive constant. We first obtain a sufficient condition for the existence of a unique nonnegative periodic solution [formula] of the associated unforced differential equation of Eq. (*) [formula] (**) Then we obtain a sufficient condition so that every nonnegative solution of the forced equation (*) converges to this nonnegative periodic solution [formula] of the associated unforced equation (**). Applications from mathematical biology and numerical examples are also given.
4
Content available Oscillation criteria for third order nonlinear delay differential equations with damping
Grace S. R.
Opuscula Mathematica
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2015
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Vol. 35, no. 4
485--497
EN
This note is concerned with the oscillation of third order nonlinear delay differential equations of the form (r2(t) (r1(t)y'(t))')' +p(t)y'(t) + q(t)ƒ(y(g(t))) = 0. (*) In the papers [A.Tiryaki, M.F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007), 54-68] and [M.F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear-functional differential equations, Applied Math. Letters 23 (2010), 756-762], the authors established some sufficient conditions which insure that any solution of equation (*) oscillates or converges to zero, provided that the second order equation (r2(t)z'(t))' + (p(t)/r1(t))z(t) =0 (**) is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (*) oscillates if equation (**) is nonoscillatory. We also establish results for the oscillation of equation (*) when equation (**) is oscillatory.
5
Content available Stabilisation of LC ladder network with the help of delayed output feedback
Baranowski J., Mitkowski W.
Control and Cybernetics
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2012
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Vol. 41, no. 1
13-34
EN
The paper presents a method of stabilisation of an LC ladder network with a delayed output feedback. A discussion of certain properties of tridiagonal matrices and formulation of the considered system in state space equations is included. Formal stability of the arising infinite dimensional system is described and stability conditions are formulated based on properties of characteristic quasipolynomial. The method of D-partitions is used to determine the stability regions in the controller parameter space. Paper includes examples for ladders of dimensions 1, 2 and 3 and a comparison with Padé approximation.
6
Content available remote Asymptotic behaviour of oscillatory solutions of n-th order differnetial equations
Padhi S.
Fasciculi Mathematici
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2007
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Nr 37
49-55
EN
In this paper, sufficient conditions have been obtained so that all oscillatory solutions of the n-th order differential equations with quasi derivatives tend to zero as t tends to infinity.
7
Content available remote Asymptotic behavior of solutions of impulsive differential equations with positive and negative coefficients
Wei G., Shen J.
Fasciculi Mathematici
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2005
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Nr 36
109-119
EN
This paper is concerned with the impulsive delay differential equations with positive and negative coefficients Sufficient conditions are obtained for every solution of the above equation tends to a constant as t —> &infin. KEY WORDS: asymptotic behavior, Liapunov functional, delay differential equation, impulse, coefficients.
8
Content available remote Logistic Equations in Tumour Growth Modelling
Foryś U., Marciniak-Czochra A.
International Journal of Applied Mathematics and Computer Science
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2003
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Vol. 13, no 3
317-325
EN
The aim of this paper is to present some approaches to tumour growth modelling using the logistic equation. As the first approach the well-known ordinary differential equation is used to model the EAT in mice. For the same kind of tumour, a logistic equation with time delay is also used. As the second approach, a logistic equation with diffusion is proposed. In this case a delay argument in the reaction term is also considered. Some mathematical properties of the presented models are studied in the paper. The results are illustrated using computer simulations.
9
Content available remote Behaviour of Solutions to Marchuk's Model Depending on a Time Delay
Bodnar M., Foryś U.
International Journal of Applied Mathematics and Computer Science
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2000
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Vol. 10, no 1
97-112
EN
Marchuk's model of an immune reaction is a system of differential equations with a time delay. The aim of this paper is to study the behaviour of solutions to Marchuk's model depending upon the delay of immune reaction and the history of an illness. We study Marchuk's model without delays, with aconstant delay and with an infinite delay. A continuous dependence on thedelay is considered. Bifurcation points are found using computer simulations.
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