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Wyświetlanie 1-15 z 33
Tytuł:
Travelling waves for low-grade glioma growth and response to a chemotherapy model
Autorzy:
Bartłomiejczyk, Agnieszka
Bodnar, Marek
Bogdańska, Magdalena U.
Piotrowska, Monika J.
Powiązania:
https://bibliotekanauki.pl/articles/24202933.pdf
Data publikacji:
2023
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
low grade glioma
generalized model
partial differential equation
wave solution
chemotherapy model
glejak
model uogólniony
równanie różniczkowe cząstkowe
rozwiązanie falowe
model chemioterapii
Opis:
Low-grade gliomas (LGGs) are primary brain tumours which evolve very slowly in time, but inevitably cause patient death. In this paper, we consider a PDE version of the previously proposed ODE model that describes the changes in the densities of functionally alive LGGs cells and cells that are irreversibly damaged by chemotherapy treatment. Besides the basic mathematical properties of the model, we study the possibility of the existence of travelling wave solutions in the framework of Fenichel’s invariant manifold theory. The estimates of the minimum speeds of the travelling wave solutions are provided. The obtained analytical results are illustrated by numerical simulations.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2023, 33, 4; 569--581
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Critical cases in neutral functional differential equations, arising from hydraulic engineering
Autorzy:
Răsvan, Vladimir
Powiązania:
https://bibliotekanauki.pl/articles/2216162.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
1D hyperbolic partial differential equations
neutral functional differential equation
difference operator
critical case
differential equations
Opis:
This paper starts from several applications described by initial/boundary value problems for 1D (time and one space variable) hyperbolic partial differential equations whose basic properties and stability of equilibria are studied throughout the same properties for certain associated neutral functional differential equations. It is a common fact that asymptotic stability for neutral functional differential equations is normally obtained under the assumption of asymptotic stability of the difference operator associated to the aforementioned neutral functional differential equations. However the physically meaningful applications presented in the paper have the associated difference operator(s) in critical cases (their stability is, generally speaking, non-asymptotic). Consequently the stability of the considered application models is either non-asymptotic or fragile (in a sense introduced in the paper). The models represent an overview gathered from various fields, processed here in order to emphasize the associated neutral functional differential equations which, consequently, are a challenge to the usual approaches. In the concluding part there are suggested possible ways to overcome these difficulties.
Źródło:
Opuscula Mathematica; 2022, 42, 4; 605-633
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical scheme methods for solving nonlinear pseudo-hyperbolic partial differential equations
Autorzy:
Abdulazeez, Sadeq Taha
Modanli, Mahmut
Husien, Ahmad Muhamad
Powiązania:
https://bibliotekanauki.pl/articles/2202054.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
nonlinear pseudo-hyperbolic partial differential equation
homotopy analysis method
variational iteration method
approximate solution
nieliniowe pseudohiperboliczne równanie różniczkowe cząstkowe
homotopijna metoda analizy
metoda iteracji wariacyjnych
rozwiązanie przybliżone
Opis:
The numerical solutions to the nonlinear pseudo-hyperbolic partial differentia equation with nonlocal conditions are presented in this study. This equation is solved using the homotopy analysis technique (HAM) and the variational iteration method (VIM). Both strategies are compared and contrasted in terms of approximate and accurate solutions. The results show that the HAM technique is more appropriate, effective, and close to the exact solution than the VIM method. Finally, the graphical representations of the obtained results are given.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 4; 5--15
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On classical symmetries of ordinary differential equations related to stationary integrable partial differential equations
Autorzy:
Tsyfra, Ivan
Powiązania:
https://bibliotekanauki.pl/articles/2050893.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
ordinary differential equation
partial differential equation
integrability
symmetry
quadrature
Lie transformation group
Opis:
We study the relationship between the solutions of stationary integrable partial and ordinary differential equations and coefficients of the second-order ordinary differen¬tial equations invariant with respect to one-parameter Lie group. The classical symmetry method is applied. We prove that if the coefficients of ordinary differential equation satisfy the stationary integrable partial differential equation with two independent variables then the ordinary differential equation is integrable by quadratures. If special solutions of integrable partial differential equations are chosen, then the coefficients satisfy the stationary KdV equations. It was shown that the Ermakov equation belong to a class of these equations. In the framework of the approach we obtained the similar results for generalized Riccati equations. By using operator of invariant differentiation we describe a class of higher order ordinary differential equations for which the group-theoretical method enables us to reduce the order of ordinary differential equation.
Źródło:
Opuscula Mathematica; 2021, 41, 5; 685-699
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional heat conduction in a rectangular plate with bending moments
Autorzy:
Warbhe, Shrikant
Powiązania:
https://bibliotekanauki.pl/articles/1839729.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Mittag-Leffler function
integral transform
fractional partial differential equation
fractional derivatives
fractional integrals
ułamkowe równanie różniczkowe cząstkowe
funkcja Mittag-Lefflera
pochodna ułamkowa
naprężenia termiczne
przewodzenia ciepła
transformata całkowa
Opis:
In this research work, we consider a thin, simply supported rectangular plate defined as 0 ≤ x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ c and determine the thermal stresses by using a thermal bending moment with the help of a time dependent fractional derivative. The constant temperature is prescribed on the surface y = 0 and other surfaces are maintained at zero temperature. A powerful technique of integral transform is used to find the analytical solution of initial-boundary value problem of a thin rectangular plate. The numerical result of temperature distribution, thermal deflection and thermal stress component are computed and represented graphically for a copper plate.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 115-126
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fractional heat conduction in a rectangular plate with bending moments
Autorzy:
Warbhe, Shrikant
Powiązania:
https://bibliotekanauki.pl/articles/1839752.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Mittag-Leffler function
integral transform
fractional partial differential equation
fractional derivatives
fractional integrals
ułamkowe równanie różniczkowe cząstkowe
funkcja Mittag-Lefflera
pochodna ułamkowa
naprężenia termiczne
przewodzenia ciepła
transformata całkowa
Opis:
In this research work, we consider a thin, simply supported rectangular plate defined as 0 ≤ x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ c and determine the thermal stresses by using a thermal bending moment with the help of a time dependent fractional derivative. The constant temperature is prescribed on the surface y = 0 and other surfaces are maintained at zero temperature. A powerful technique of integral transform is used to find the analytical solution of initial-boundary value problem of a thin rectangular plate. The numerical result of temperature distribution, thermal deflection and thermal stress component are computed and represented graphically for a copper plate.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 115-126
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stabilized model reduction for nonlinear dynamical systems through a contractivity-preserving framework
Autorzy:
Chaturantabut, Saifon
Powiązania:
https://bibliotekanauki.pl/articles/1838159.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
model order reduction
ordinary differential equation
partial differential equation
proper orthogonal decomposition
discrete empirical interpolation method
redukcja rzędu modelu
równanie różniczkowe zwyczajne
równanie różniczkowe cząstkowe
rozkład ortogonalny
Opis:
This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2020, 30, 4; 615-628
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Partial linear homogeneous differential equations of the first order and Matheamtica
Równania różniczkowe cząstkowe liniowe jednorodne rzędu pierwszego i program Mathematica
Autorzy:
Czajkowski, Andrzej Antoni
Oleszak, Wojciech Kazimierz
Powiązania:
https://bibliotekanauki.pl/articles/135794.pdf
Data publikacji:
2019
Wydawca:
Wyższa Szkoła Techniczno-Ekonomiczna w Szczecinie
Tematy:
partial differential equation
solutions
Mathematica
równanie różniczkowe cząstkowe
rozwiązania
Opis:
Introduction and aims: The paper describes the method of solving first order linear differential homogeneous differential equations using Mathematica program. The purpose of the work is to provide algorithms for analytical and symbolic solutions in Mathematica for three selected examples. Material and methods: The work uses selected literature from first order linear partial differential equations. The method of characteristics was used in analytical solutions, and the Mathematica 5 program in numerical solutions. Results: The characteristics method was used in analytical solutions of selected examples of first order linear partial differential equations. In addition to numerical solutions, graphic interpretation was given using spatial and contour charts. Conclusion: Mathematica program solves the first order linear partial differential equations with given boundary conditions using the pde and DSolve procedures. Mathematica program also allows for first order linear partial differential equations with boundary conditions to show some geometric interpretation of their solutions using the Plot3D and ContourPlot commands.
Wstęp i cele: W pracy opisano metodę rozwiązywania równań różniczkowych cząstkowych liniowych jednorodnych pierwszego rzędu z wykorzystaniem programu Mathematica. Celem pracy jest podanie algorytmów rozwiązań analitycznych i symbolicznych w programie Mathematica dla wybranych trzech różnych przykładów. Materiał i metody: W pracy wykorzystano wybraną literaturę z równań różniczkowych cząstkowych liniowych rzędu pierwszego. W rozwiązaniach analitycznych zastosowano metodę charakterystyk, a w rozwiązaniach numerycznych program Mathematica 5. Wyniki: Metodę charakterystyk zastosowano w rozwiązaniach analitycznych wybranych przykładów równań różniczkowych cząstkowych liniowych rzędu pierwszego. Oprócz rozwiązań numerycznych podano interpretację graficzną stosując wykresy przestrzenne i konturowe. Wnioski: Program Mathematica rozwiązuje liniowe jednorodne równania różniczkowe cząstkowe pierwszego rzędu z zadanymi warunkami brzegowymi stosując procedury pde i DSolve. Program Mathematica umożliwia również dla równań różniczkowych cząstkowych liniowych rzędu pierwszego z warunkami brzegowymi pokazanie geometrycznej interpretacji ich rozwiązań za pomocą poleceń Plot3D i ContourPlot.
Źródło:
Problemy Nauk Stosowanych; 2019, 10; 5-14
2300-6110
Pojawia się w:
Problemy Nauk Stosowanych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical Solution to Linear Conformable Fractional Partial Differential Equations
Autorzy:
Dixit, Ajay
Ujlayan, Amit
Powiązania:
https://bibliotekanauki.pl/articles/1159232.pdf
Data publikacji:
2018
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Conformable fractional derivative
Fractional partial differential equation
Katugampola’s derivative
Method of separation of variables
Opis:
An analytical solution is better than an approximate or series solution of a problem. Here we develop an analytical formulation to solve linear fractional order partial differential equations with given boundary conditions. We discuss the method for the simultaneous fractional derivative, in space as well as time and up to order two. Examples reflect the effectiveness and simplicity of the method. First we convert the fractional derivative into integer order derivative and then use method of separation of variables in usual sense to get the complete solution. The fractional derivative has been taken in the sense of Katugampola’s derivative.
Źródło:
World Scientific News; 2018, 113; 49-56
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion
Autorzy:
Tagade, P. M.
Choi, H. L.
Powiązania:
https://bibliotekanauki.pl/articles/330516.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Bayesian framework
stochastic partial differential equation
Karhunen–Loève expansion
generalized polynomial chaos
dynamically biorthogonal field equations
ramy Bayesa
stochastyczne równanie różniczkowe
przekształcenie Karhunena-Loeve'a
chaos wielomianowy
Opis:
This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen–Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 2; 229-243
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient
Autorzy:
Farahani, H. S.
Telabi, H. A.
Baghermenhaj, M.
Powiązania:
https://bibliotekanauki.pl/articles/229317.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
drilling systems
adaptive control
hyperbolic partial differential equations
wave equation
boundary control
Opis:
The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.
Źródło:
Archives of Control Sciences; 2017, 27, 1; 63-76
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Feedback design of differential equations of reconstruction for second-order distributed parameter systems
Autorzy:
Maksimov, V. I.
Mordukhovich, B. S.
Powiązania:
https://bibliotekanauki.pl/articles/330817.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
partial differential equation
equations of reconstruction
distributed parameter system
równanie różniczkowe cząstkowe
układ o parametrach rozłożonych
równanie drugiego rzędu
Opis:
The paper aims at studying a class of second-order partial differential equations subject to uncertainty involving unknown inputs for which no probabilistic information is available. Developing an approach of feedback control with a model, we derive an efficient reconstruction procedure and thereby design differential equations of reconstruction. A characteristic feature of the obtained equations is that their inputs formed by the feedback control principle constructively approximate unknown inputs of the given second-order distributed parameter system.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 467-475
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Properties of entire solutions of some linear PDEs
Autorzy:
Bandura, A,
Skaskiv, O.
Filevych, P.
Powiązania:
https://bibliotekanauki.pl/articles/122451.pdf
Data publikacji:
2017
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
linear partial differential equation
entire function
bounded L-index in direction
bounded l-index
homogeneous linear differential equation
growth of solutions
liniowe równanie różniczkowe cząstkowe
funkcja całkowita
równanie różniczkowe cząstkowe
Opis:
In this paper, there are improved sufficient conditions of boundedness of the L-index in a direction for entire solutions of some linear partial differential equations. They are new even for the one-dimensional case and L≡1. Also, we found a positive continuous function l such that entire solutions of the homogeneous linear differential equation with arbitrary fast growth have a bounded l -index and estimated its growth.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 2; 17-28
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Topological sensitivity analysis for a coupled nonlinear problem with an obstacle
Autorzy:
Abdelbari, M.
Nachi, K.
Sokolowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/205653.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
topological derivative
shape optimization
SteklovPoincaroperator
Signorini problem
variational inequality
Helmholtz equation
coupled partial differential equations
conical differential
asymptotic expansions
singular perturbations of geometrical Romains
truncated domain
Opis:
The Topological Derivative has been recognized as a powerful tool in obtaining the optimal topology for several kinds of engineering problems. This derivative provides the sensitivity of the cost functional for a boundary value problem for nucleation of a small hole or a small inclusion at a given point of the domain of integration. In this paper, we present a topological asymptotic analysis with respect to the size of singular domain perturbation for a coupled nonlinear PDEs system with an obstacle on the boundary. The domain decomposition method, referring to the SteklovPoincar´epseudo-differential operator, is employed for the asymptotic study of boundary value problem with respect to the size of singular domain perturbation. The method is based on the observation that the known expansion of the energy functional in the ring coincides with the expansion of the Steklov-Poincar´e operator on the boundary of the truncated domain with respekt to the small parameter, which measures the size of perturbation. In this way, the singular perturbation of the domain is reduced to the regular perturbation of the Steklov-Poincar´e map ping for the ring. The topological derivative for a tracking type shape functional is evaluated so as to obtain the useful formula for application in the numerical methods of shape and topology optimization.
Źródło:
Control and Cybernetics; 2017, 46, 1; 5-25
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Nash equilibrium approach for multiobjective optimal control problems with elliptic partial differential equations
Autorzy:
Dreves, A.
Powiązania:
https://bibliotekanauki.pl/articles/206122.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
multiobjective optimization
generalized Nash equilibrium
optimal control problem
elliptic partial differential equation
finite elements
interior point method
Opis:
We consider the generalized Nash equilibrium as a solution concept for multiobjective optimal control problems governed by elliptic partial differential equations with constraints not only for the control but also for the state variables. In the first part, we present a constructive proof of the existence of a generalized Nash equilibrium via an approximating sequence of suitable finite dimensional discretizations. In the second part, we propose a variant of a potential reduction algorithm for the numerical solution of these discretized problems. In contrast to the existing numerical approaches ours does not require the computation of the control–to–state mapping. Instead we introduce different state variables and guarantee that they become equal at a solution. We prove sufficient conditions for the convergence of our algorithm to a solution. Furthermore, some numerical results showing the applicability are provided.
Źródło:
Control and Cybernetics; 2016, 45, 4; 457-482
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
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