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1
Content available remote Using Euler’s and Taylor’s expansion method for solution of non-linear differential equation system in pharmacokinetics
Beňová M., Gombárska D., Dobrucký B.
Przegląd Elektrotechniczny
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2013
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R. 89, nr 2a
259--261
EN
The paper deals with Euler's- and Taylor's expansion methods for next numerical solution in Matlab environment. There are many applications in pharmacokinetic described and modelled by linear or non-linear differential equation (DE) systems. These non-linarities can be considered in drug absorption, distribution, metabolism and excretion, and the pharmacokinetics of drug action. A fictitious exciting functions method makes possible numerical solution of this DE system with non-stationary matrices. The solutions of simple example are presented as well.
PL
Praca pokazuje zastosowanie rozwinięcia Eulera i Taylora w rozwiązaniu równań różniczkowych zwyczajnych w środowisku Matlaba. W szczególności rozważono równania różniczkowe liniowe i nieliniowe zapisane w formie równań stanu. Symulacje numeryczne potwierdzające prawidłowość proponowanej metody dotyczyły praktycznego przykłady równań farmakokinetycznych występujących przy badaniach leku stosowanego w angioplastyce wieńcowej.
2
Transverse diffraction of weakly nonlinear waves for a first order quasi-linear system involving source-like terms
Conforto F., Giambo S., Valenti G.
Journal of Technical Physics
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2004
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Vol. 45, no 1
55-69
EN
Making use of the ray theory and the method of asymptotic expansion of multiple scales, a study of the diffraction of weakly nonlinear waves in a direction transverse to the rays, through media described by dissipative or dispersive hyperbolic systems, is proposed. It is shown that the wave amplitude satisfies a generalized Zabolotskaya-Khokhlov equation in the dissipative case, or a generalized Kadomtsev-Petviashvili equation in the dispersive case. Moreover, plane, cylindrical and spherical waves are also investigated. The present approach is used to study wave diffraction in a heat-conducting fluid.
3
Vibrations of the complex torsional system with a viscoelastic mass interlayer
Cabańska-Płaczkiewicz K., Pankratova N. D.
Journal of Technical Physics
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2002
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Vol. 43, no 2
205-217
EN
This paper presents an analytical method of solving the free and forced vibrations problems concerning a complex torsional continuous system of two circular shafts connected by a viscoelastic mass interlayer. In the solution of free and forced vibrations; the complex functions of real variable are used. Then, the property of orthogonality of complex modes of free vibrations has been demonstrated which is the basis for solving the free and forced vibrations problem for arbitrary initial conditions. The small torsional vibrations of the complex system with a viscoelastic mass interlayer are excited by the steady-state dynamical loading.
4
Adomian's approach to coupled non-linear differential equations
Wyrwał J.
Zeszyty Naukowe. Matematyka / Politechnika Opolska
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2001
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z. 17
119-123
EN
The simple system of coupled non-linear differential equation is solved by the (Adomian) decomposition method which provides an analytical approximation requiring no linearization. The method presents a new approach to non-linear problems.
PL
Przy wykorzystaniu metody dekompozycji (Adomiana) rozwiązano prosty układ nieliniowych równań różniczkowych zwyczajnych, uzyskując analityczną aproksymację rozwiązania bez konieczności linearyzacji równań wyjściowych.
5
Nonlinear regular and chaotic dynamics of a helicopter
Dżygadło Z., Kowaleczko G.
Journal of Technical Physics
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2001
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Vol. 42, no 2
241-268
EN
A helicopter is a rotorcraft, which can be subjected, during its motion, to various types of vibrations. This paper presents selected results of analysis of these vibrations. It is carried out on the basis of the complete set of nonlinear differential equations describing the helicopter fuselage motion and all the blades motions. For the helicopter performing a steady-state flight, the control law for static autopilot is formulated on the basis of the method of motions separation. In the case of a ground resonance the forces and moments produced by a landing gear are taken into consideration. The flutter phenomenon is also simulated. Some results of numerical analysis are presented, which show that some oscillations are regular and others have rather a chaotic character.
6
Content available remote Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations
Graef J. R., Thandapani E.
Fasciculi Mathematici
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2001
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Nr 31
23-36
EN
The authors consider the nonlinear difference equation (E) delta2 ((delta(bn delta yn))+f(n,yn-t)=0, n należy N(no)={no,no+1,...}, here {an} and {bn} are positive real sequences, I is a nonnegative integer, f: N(no) x R R is a continuous function with uf(n, u) > 0 for all u nierówne 0. They obtain necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior. They also obtain sufficient conditions for all solutions to be oscillatory if/ is either strongly sublinear or strongly superlinear. Examples of their results are also included.
7
Content available remote On the asymptotic behaviour of solutions of nonlinear difference equations
Migda M., Schmeidel E.
Fasciculi Mathematici
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2001
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Nr 31
63-69
EN
This paper consists of three theorems. For the nonlinear difference equation (E) wzór sufficient conditions for the existence of the asymptotically constant solutions are given in Th. 1. In Th. 2 conditions under which there exists a solution (xn) of Eq. (E) such that xn = cn + o(1), are given. In Th. 3 conditions under which every solution (xn) of Eq. (E) possesses property: the sequence (xn/n is convergent in R, are presented.
8
Content available remote On asymptotic behaviour and oscillation of forced first order nonlinear neutral difference equations
Parhi N., Tripathy A. K.
Fasciculi Mathematici
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2001
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Nr 32
83-95
EN
Oscillatory and asymptotic behaviour of solutions of forced first order nonlinear neutral delay difference equations of the from (mathematical formula) is studied under appropriate assumptions on sequences of real numbers {qn} and {q(n) {f(n)} and {fn} and G belong to class C(R, R). The behaviour of solutions of mathematical formula is also discussed where {pa} is allowed to change sign.
9
Content available remote Asymptotic behaviour of solutions of nonlinear delay difference equations
Migda M.
Fasciculi Mathematici
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2001
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Nr 31
57-62
EN
Asymptoic properties of the solutions of the difference equation of the form ^(r(n-1)^x(n-1))+anf(x(n-k)=bn are studied.
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