Browsing by Subject "finite difference method"

Now showing 1 - 10 of 10

Access status: Open Access ,
A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
(2007) Malec, Marian; Sapa, Lucjan
This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in $\mathbf{R}^{1+n}$. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
Access status: Open Access ,
Can artificial intelligence predict a tsunami?
(Wydawnictwa AGH, 2026) Wójcik, Daria; Niewiadomska, Alicja; Paszyński, Maciej
In this article, we build a model for tsunami simulation based on physicsinformed neural networks and the Finite Difference Method. We then check how the numerical results obtained using these two methods differ from each other. Assuming that the Finite Difference Method gives accurate results, we estimate the error resulting from the use of physics-informed neural networks. We compare this estimate with surveys conducted among computer science students in order to assess the level of public trust among specialists in the numerical results obtained using artificial intelligence tools. In particular, we assess how reliable tsunami predictions obtained using physics-informed neural networks are and what the public perception of the reliability of such predictions is.
Access status: Restricted ,
Iteracyjna metoda wyceny opcji amerykańskich
(Data obrony: 2018-07-18) Krawczyk, Gabriela
Wydział Matematyki Stosowanej
Access status: Restricted ,
Metoda różnic skończonych i elementów skończonych dla hiperbolicznych
(Data obrony: 2017-07-18) Białas, Katarzyna
Wydział Matematyki Stosowanej
Access status: Restricted ,
Metody numeryczne rozwiązywania równań hiperbolicznych
(Data obrony: 2011-07-11) Koperska, Katarzyna
Wydział Matematyki Stosowanej
Access status: Open Access ,
Numerical approaches to the heat transfer problem in modern electronic structures
(Wydawnictwa AGH, 2017) Raszkowski, Tomasz; Samson, Agnieszka
The main aim of this paper is to present a detailed description of the research related to the modeling of heat conduction in modern electronic structures, including special consideration for numerical aspects of analyzed algorithms. The motivation to undertake the research as well as some of the most-important results of the experiments and simulations are also included. Moreover, a numerical approximation of the problem as well as the methodology used and a sample solution of the mentioned problem are presented. In the main part, the discretization techniques, Ordinary Differential Equation algorithms, and simulation results for Runge-Kutta’s and Gear’s algorithms are analyzed and discussed. Additionally, a new effective approach to the modeling of heat transfer in electronic nanostructures is demonstrated.
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Porównawcze badania modelowe filtracji wód podziemnych metodami różnic skończonych i elementów skończonych
(Data obrony: 2017-09-26) Świerczek, Małgorzata
Wydział Geologii, Geofizyki i Ochrony Środowiska
Praca skupia się na analizie porównawczej metodyki badań modelowych oraz wyników symulacji prowadzonych metodami różnic skończonych i elementów skończonych z wykorzystaniem programów Processing Modflow 8 oraz Feflow 7.0. Badania były prowadzone na modelu hipotetycznego systemu wodonośnego, reprezentującego typowe warunki dolinne w dwóch wariantach zagęszczenia siatki dyskretyzacyjnej dla każdej z metod. Rezultaty przeprowadzonych symulacji przedstawiono w formie zestawień globalnych bilansów wodnych oraz map zwierciadła wody i depresji. Uzyskane w poszczególnych metodach wyniki bilansowe nieznacznie się różnią, w zależności od rozpatrywanego składnika, natomiast rozkłady pola hydrodynamicznego i wielkości depresji w obu metodach wykazują bardzo duże podobieństwo.
Access status: Restricted ,
Wpływ warunków brzegowych na modelowanie pełnego pola falowego
(Data obrony: 2011-07-15) Hadro, Grzegorz
Wydział Geologii, Geofizyki i Ochrony Środowiska
The aim of this thesis is to define differences occurred on model's bounds after use boundary conditions for values of wavefield considering various differential sachems. Differential schemes of 2nd and 4th order was determined with using two the most common boundary conditions: absorbing and reflective bound. Software written by author was used for modelling wavefield. Program has a window interface which allows to submit desired geological model based on velocity of wave in various environments. For check and comparison differences in results MatLab software was used. The conclusion was built on analyses of received data.
Access status: Restricted ,
Wycena opcji metodą różnic skończonych w Modelu Blacka-Scholesa
(Data obrony: 2011-10-27) Radwan, Dawid
Wydział Matematyki Stosowanej
Access status: Restricted ,
Wycena opcji metodą różnic skończonych w Modelu Blacka-Scholesa
(Data obrony: 2011-10-27) Radwan, Dawid
Wydział Matematyki Stosowanej