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Wyświetlanie 1-15 z 33
Tytuł:
Modelling Tumour-Immunity Interactions With Different Stimulation Functions
Autorzy:
Zhivkov, P.
Waniewski, J.
Powiązania:
https://bibliotekanauki.pl/articles/908163.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
medycyna
matematyka
ordinary differential equations
critical points
stability analysis
immunotherapy
Opis:
Tumour immunotherapy is aimed at the stimulation of the otherwise inactive immune system to remove, or at least to restrict, the growth of the original tumour and its metastases. The tumour-immune system interactions involve the stimulation of the immune response by tumour antigens, but also the tumour induced death of lymphocytes. A system of two non-linear ordinary differential equations was used to describe the dynamic process of interaction between the immune system and the tumour. Three different types of stimulation functions were considered: (a) Lotka-Volterra interactions, (b) switching functions dependent on the tumour size in the Michaelis-Menten form, and (c) Michaelis-Menten switching functions dependent on the ratio of the tumour size to the immune capacity. The linear analysis of equilibrium points yielded several different types of asymptotic behaviour of the system: unrestricted tumour growth, elimination of tumour or stabilization of the tumour size if the initial tumour size is relatively small, otherwise unrestricted tumour growth, global stabilization of the tumour size, and global elimination of the tumour. Models with switching functions dependent on the tumour size and the tumour to the immune capacity ratio exhibited qualitatively similar asymptotic behaviour.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 307-315
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On strongly monotone flows
Autorzy:
Walter, Wolfgang
Powiązania:
https://bibliotekanauki.pl/articles/1294817.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
system of ordinary differential equations
initial value problem
comparison theorem
monotone flow
quasimonotonicity
Opis:
M. Hirsch's famous theorem on strongly monotone flows generated by autonomous systems u'(t) = f(u(t)) is generalized to the case where f depends also on t, satisfies Carathéodory hypotheses and is only locally Lipschitz continuous in u. The main result is a corresponding Comparison Theorem, where f(t,u) is quasimonotone increasing in u; it describes precisely for which components equality or strict inequality holds.
Źródło:
Annales Polonici Mathematici; 1997, 66, 1; 269-274
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Une fonction β-lipschitzienne qui n'est pas une perturbation compacted'une fonction dissipative
Autorzy:
Uhl, Roland
Powiązania:
https://bibliotekanauki.pl/articles/1311540.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
ordinary differential equations in Banach spaces
existence
measures of noncompactness
dissipative operators
Opis:
Résumé. On présente une fonction continue f: c₀ → c₀ qui satisfait à une condition lipschitzienne par rapport à la mesure de non-compacité de Hausdorff (ou Kuratowski), mais telle que f n'est pas la somme d'une fonction dissipative et d'une fonction compacte. Cet exemple attache de l'importance au théorème d'existence de Sabina Schmidt (1989) pour des équations différentielles dans les espaces de Banach.
Źródło:
Annales Polonici Mathematici; 1995, 61, 2; 189-193
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Do not let the dead bite! Different scenarios of the zombie epidemic reexamined
Autorzy:
Tomczyk, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/1034349.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
Tematy:
Kermack – McKendrick model
Zombie
epidemic
ordinary differential equations
Opis:
The Zombie Epidemic is a fun framework for investigating different scenarios of spreading disease. An extended Kermack – McKendrick model is analyzed. The only thing that can save humanity is to not get bitten or to find a remedy for the ”zombie virus” (both almost impossible).
Źródło:
Zeszyty Naukowe Towarzystwa Doktorantów Uniwersytetu Jagiellońskiego. Nauki Ścisłe; 2015, 11; 21-33
2082-3827
2084-977X
Pojawia się w:
Zeszyty Naukowe Towarzystwa Doktorantów Uniwersytetu Jagiellońskiego. Nauki Ścisłe
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP
Autorzy:
Rauh, A.
Brill, M.
Günther, C.
Powiązania:
https://bibliotekanauki.pl/articles/930113.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
równanie różniczkowe
symulacja sprawdzona
sterowanie odwrotne
ordinary differential equations
differential algebraic equations
VALENCIA-IVP
verified simulation
inverse control problems
Opis:
The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differential-algebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on VALENCIA-IVP, which has been developed recently for the computation of verified enclosures of the solution sets of initial value problems for ordinary differential equations. For the application to DAEs, VALENCIA-IVP has been extended by an interval Newton technique to solve nonlinear algebraic equations in a guaranteed way. In addition to verified simulation of initial value problems for DAE systems, the developed approach is applicable to the verified solution of the so-called inverse control problems. In this case, guaranteed enclosures for valid input signals of dynamical systems are determined such that their corresponding outputs are consistent with prescribed time-dependent functions. Simulation results demonstrating the potential of VALENCIA-IVP for solving DAEs in technical applications conclude this paper. The selected application scenarios point out relations to other existing verified simulation techniques for dynamical systems as well as directions for future research.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 3; 381-397
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Using Shehu integral transform to solve fractional order Caputo type initial value problems
Autorzy:
Qureshi, Sania
Kumar, Prem
Powiązania:
https://bibliotekanauki.pl/articles/122809.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformata Laplace'a
całka Riemann-Liouville
Opis:
In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential nt h order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 75-83
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A method for determination of flow at the plane, horizontal interface separating streams of two different fluids
Autorzy:
Prosnak, W. J.
Cześnik, P. P.
Powiązania:
https://bibliotekanauki.pl/articles/241051.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
interface
almost parallel streams of two fluids
boundary layer
ordinary differential equations
matching conditions
Opis:
The paper deals with the theoretical investigation of the phenomenon, which consists in generation - by wind - of the movement of water, the bodies of air and of water being separated by a horizontal, plane interface, which is identical with the free surface of water. A set of assumptions defining a physical model of the phenomenon, borrowed from Lock (1951), is introduced, as well as the mathematical description of this model. It reduces to a composite ordinary differential problem, containing two non-linear equations of the third order, which have to satisfy some boundary conditions. A novel method of solution of the differential problem just mentioned is presented in the paper. In the method use is made of exact formulae for coefficients of series representing the solution. The method seems to be competitive with the one given in the paper by Lock (1951).
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2005, 52, 2; 89-110
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A singular initial value problem for the equation $u^{(n)}(x) = g(u(x))$
Autorzy:
Mydlarczyk, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/1294503.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
singular initial value problems for ordinary differential equations
Volterra type integral equations
blowing up solutions
Opis:
We consider the problem of the existence of positive solutions u to the problem $u^{(n)}(x) = g(u(x))$,
$u(0) = u'(0) = ... = u^{(n-1)}(0) = 0$ (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition $∫₀^δ 1/s [s/g(s)]^{1/n} ds < ∞$ is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.
Źródło:
Annales Polonici Mathematici; 1998, 68, 2; 177-189
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Smoothness of unordered curves in two-dimensional strongly competitive systems
Autorzy:
Mierczyński, Janusz
Powiązania:
https://bibliotekanauki.pl/articles/1338935.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
strongly competitive system of ordinary differential equations
invariant manifold
d-curve
Lotka-Volterra system
Opis:
It is known that in two-dimensional systems of ODEs of the form $\dotx^i=x^if^i(x)$ with ${\partial f^i}/{\partial x^j} < 0$ (strongly competitive systems), boundaries of the basins of repulsion of equilibria consist of invariant Lipschitz curves, unordered with respect to the coordinatewise (partial) order. We prove that such curves are in fact of class $C^1$.
Źródło:
Applicationes Mathematicae; 1998-1999, 25, 4; 449-455
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Series Solution of Nonlinear Ordinary Differential Equations Using Single Laplace Transform Method in Mathematical Physics
Autorzy:
Mbagwu, JP. C.
Madububa, B. I.
Nwamba, J. I.
Powiązania:
https://bibliotekanauki.pl/articles/1193352.pdf
Data publikacji:
2021
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Adomian polynomials
Single Laplace transform method
nonlinear ordinary differential equations
Opis:
In this paper, a novel technique is created to enable the extension of the single Laplace transform method (SLTM) to solve nonlinear ordinary differential equations (ODEs) is presented. The main parts of the recommended technique are the Adomian polynomials. By developing several theorems, which include the Laplace transformation of nonlinear expressions, the Adomian polynomials are made possible. Several famous nonlinear equations including the Blasius equation, the Poisson Boltzmann equation, and numerous extra problems relating nonlinearities of many types such as exponential and sinusoidal are resolved for description. As it was revealed in the specified equations, and problems, our technique is conceptually and computationally simple. Some nonlinear examples are taken from the literature for checking the validation and convergence of the proposed technique. The suggested method is methodical, precise, then restricted to integration.
Źródło:
World Scientific News; 2021, 154; 152-174
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solving boundary value problems in the open source software R: package bvpSolve
Autorzy:
Mazzia, F.
Cash, J. R.
Soetaert, K.
Powiązania:
https://bibliotekanauki.pl/articles/255850.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
ordinary differential equations
boundary value problems
singular perturbation problems
test problems
Fortran
R
Opis:
The R package bvpSolve for the numerical solution of Boundary Value Problems (BVPs) is presented. This package is free software which is distributed under the GNU General Public License, as part of the R open source software project. It includes some well known codes to solve boundary value problems of ordinary differential equations (ODEs) and differential algebraic equations (DAEs). In addition to the packages already available for solving initial value problems, the new package now allows non expert users to efficiently solve boundary value problems in the problem solving environment R.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 387-403
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of the classical implicit function theorem in sensitivity analysis of parametric optimal control
Autorzy:
Malanowski, K.
Powiązania:
https://bibliotekanauki.pl/articles/206654.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równania różniczkowe nieliniowe
różniczkowalność rozwiązań
sterowanie optymalne parametryczne
differentiability of solutions
implicit function theorem
nonlinear ordinary differential equations
parametric optimal control
state constraints
Opis:
A family {(O[sub h])} of parametric optimal control problems for nonlinear ODEs is considered. The problems are subject to pointwise inequality type state constraints. It is assumed that the reference solution is regular. The original problems (O[sub h]) are substituted by problems [...] subject to equality type constraints with the sets of activity depending on the parameter. Using the classical implicit function theorem, conditions are derived under which stationary points of [...] are Frechet differentiable functions of the parameter. It is shown that, under additional conditions, the stationary points of [...] correspond to the solutions and Lagrange multipliers of (O[sub h]9).
Źródło:
Control and Cybernetics; 1998, 27, 3; 335-352
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modelowanie komputerowe układów prostowniczych jedno- i trójfazowych z obciążeniem RL
Computational modelling one and three-phase rectifier with RL load
Autorzy:
KWATER, Tadeusz
TWARÓG, Bogusław
PĘKALA, Robert
BARTNIK, Karol
Powiązania:
https://bibliotekanauki.pl/articles/455152.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Rzeszowski
Tematy:
modelowanie komputerowe
równania różniczkowe zwyczajne
schematy połączeń obwodów elektrycznych
dioda
tyrystor
przebiegi symulacyjne
computational modelling
ordinary differential equations
scheme electrical circuits
diode
thyristor
simulation waveforms
Opis:
W artykule przedstawiono problematykę dotyczącą modelowania komputerowego układów prostowniczych jedno- i trójfazowych z obciążeniem typu RL. Podano założenia upraszczające oraz schematy połączeń elektrycznych i odpowiadające im równania różniczkowe zwyczajne. Zamieszczono rezultaty eksperymentów numerycznych potwierdzających ich zgodność z przebiegami rzeczywistymi
This paper presents issues concerning computational modelling systems one and three-phase rectifier with a load RL. Given the simplifying assumptions and the wiring diagrams and the corresponding ordinary differential equations. Contains the results of numerical experiments confirming their compliance with the actual waveforms
Źródło:
Edukacja-Technika-Informatyka; 2013, 4, 2; 351-357
2080-9069
Pojawia się w:
Edukacja-Technika-Informatyka
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
Autorzy:
Kumar, Prem
Qureshi, Sania
Powiązania:
https://bibliotekanauki.pl/articles/122736.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformacja Laplace'a
całka Riemann-Liouville
Opis:
Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
Autorzy:
Kumar, Prem
Qureshi, Sania
Powiązania:
https://bibliotekanauki.pl/articles/1839810.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformacja Laplace'a
całka Riemann-Liouville
Opis:
Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 33

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