Relevant bibliographies by topics / Aplikace parciálních diferenciálních rovnic

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Academic literature on the topic 'Aplikace parciálních diferenciálních rovnic'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Dissertations / Theses on the topic "Aplikace parciálních diferenciálních rovnic"

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Ježková, Jitka. "Modelování dopravního toku." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232180.

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Tato diplomová práce prezentuje problematiku dopravního toku a jeho modelování. Zabývá se především několika LWR modely, které následně rozebírá a hledá řešení pro počáteční úlohy. Ukazuje se, že ne pro všechny počáteční úlohy lze řešení definovat na celém prostoru, ale jen v určitém okolí počáteční křivky. Proto je dále odvozena metoda výpočtu velikosti tohoto okolí a to nejen zcela obecně, ale i pro dané modely. Teoretický rozbor LWR modelů a řešení počátečních úloh jsou demonstrovány několika příklady, které zřetelně ukazují, jak se dopravní tok simulovaný danými modely chová.
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Nečasová, Gabriela. "Paralelní numerické řešení parciálních diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2014. http://www.nusl.cz/ntk/nusl-236119.

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This thesis deals with the topic of partial differential equations parallel solutions. First, it focuses on ordinary differential equations (ODE) and their solution methods using Taylor polynomial. Another part is devoted to partial differential equations (PDE). There are several types of PDE, there are parabolic, hyperbolic and eliptic PDE. There is also explained how to use TKSL system for PDE computing. Another part focuses on solution methods of PDE, these methods are forward, backward and combined methods. There was explained, how to solve these methods in TKSL and Matlab systems. Computing accuracy and time complexity are also discussed. Another part of thesis is PDE parallel solutions. Thanks to the possibility of PDE convertion to ODE systems it is possible to represent each ODE equation by independent operation unit. These units enable parallel computing. The last chapter is devoted to implementation. Application enables generation of ODE systems for TKSL system. These ODE systems represent given hyperbolic PDE.
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Valenta, Václav. "Moderní metody řešení eliptických parciálních diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2009. http://www.nusl.cz/ntk/nusl-236712.

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Partial differential equations solution and methods for transformation to a large sets of ordinary equations is described in this work. Taylor series method is important for this work. This method needs higher derivatives for correct work. Ways how to compute higher derivatives are also discused in this work.
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Humená, Patrícia. "Adaptivní metody řešení eliptických parciálních diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2013. http://www.nusl.cz/ntk/nusl-236199.

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The objective of this project is to get familiar with the numerical solution of partial differential equations. This solution will be implemented by using a grid refinement based on the aposteriory error estimation.
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Valenta, Václav. "Řešení parciálních diferenciálních rovnic s využitím aposteriorního odhadu chyby." Doctoral thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2016. http://www.nusl.cz/ntk/nusl-412549.

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This thesis deals with gradient calculation in triangulation nodes using weighted average of gradients of neighboring elements. This gradient is then used for a posteriori error estimation which produce better solution of partial differential equations. This work presents two common methods - Finite elements method and Finite difference method.
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Havle, Oto. "Numerická analýza parciálních diferenciálních rovnic s aplikací v matematickém modelování." Doctoral thesis, 2010. http://www.nusl.cz/ntk/nusl-379602.

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Češík, Antonín. "Vlastnosti konvexního obalu pro parabolické soustavy parciálních diferenciálních rovnic." Master's thesis, 2019. http://www.nusl.cz/ntk/nusl-406311.

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The topic of this thesis is the convex hull property for systems of partial differential equations, which is a natural generalisation of the maximum principle for scalar equations. The main result of this thesis is a theorem asserting the convex hull property for the solutions of a certain class of parabolic systems of nonlinear partial differential equations. It also investigates the coefficients of linear systems. The respective results are sharp which is demonstrated by counterexamples to the convex hull property for solutions of linear elliptic and parabolic systems. The general theme is that the coupling of the system is what breaks the convex hull property, not necessarily the non-linearity.
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Bílý, Michael. "Principy maxima pro nelineární systémy eliptických parciálních diferenciálních rovnic." Master's thesis, 2017. http://www.nusl.cz/ntk/nusl-368126.

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We consider nonlinear elliptic Bellman systems which arise in the theory of stochastic differential games. The right hand sides of the equations (which are called Hamiltonians) may have quadratic growth with respect to the gradient of the unknowns. Under certain assumptions on Lagrangians (from which the Hamiltonians are derived), that are satisfied for many types of stochastic games, we establish the existence and uniqueness of a Nash point and develop structural conditions on the Hamiltonians. From these conditions we establish a certain version of maximum and minimum principle. This result is then used to establish the existence of a bound solution. 1
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Papež, Jan. "Algebraická chyba v maticových výpočtech v kontextu numerického řešení parciálních diferenciálních rovnic." Doctoral thesis, 2017. http://www.nusl.cz/ntk/nusl-267941.

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Title: Algebraic Error in Matrix Computations in the Context of Numerical Solution of Partial Differential Equations Author: Jan Papež Department: Department of Numerical Mathematics Supervisor: prof. Ing. Zdeněk Strakoš, DrSc., Department of Numerical Mathe- matics Abstract: Solution of algebraic problems is an inseparable and usually the most time-consuming part of numerical solution of PDEs. Algebraic computations are, in general, not exact, and in many cases it is even principally desirable not to perform them to a high accuracy. This has consequences that have to be taken into account in numerical analysis. This thesis investigates in this line some closely related issues. It focuses, in particular, on spatial distribution of the errors of different origin across the solution domain, backward error interpretation of the algebraic error in the context of function approximations, incorporation of algebraic errors to a posteriori error analysis, influence of algebraic errors to adaptivity, and construction of stopping criteria for (preconditioned) iterative algebraic solvers. Progress in these issues requires, in our opinion, understanding the interconnections between the phases of the overall solution process, such as discretization and algebraic computations. Keywords: Numerical solution of partial...
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Papež, Jan. "Odhady algebraické chyby a zastavovací kritéria v numerickém řešení parciálních diferenciálních rovnic." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-313457.

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Title: Estimation of the algebraic error and stopping criteria in numerical solution of partial differential equations Author: Jan Papež Department: Department of Numerical Mathematics Supervisor of the master thesis: Zdeněk Strakoš Abstract: After introduction of the model problem and its properties we describe the Conjugate Gradient Method (CG). We present the estimates of the energy norm of the error and a heuristic for the adaptive refinement of the estimate. The difference in the local behaviour of the discretization and the algebraic error is illustrated by numerical experiments using the given model problem. A posteriori estimates for the discretization and the total error that take into account the inexact solution of the algebraic system are then discussed. In order to get a useful perspective, we briefly recall the multigrid method. Then the Cascadic Conjugate Gradient Method of Deuflhard (CCG) is presented. Using the estimates for the error presented in the preceding parts of the thesis, the new stopping criteria for CCG are proposed. The CCG method with the new stopping criteria is then tested. Keywords: numerical PDE, discretization error, algebraic error, error es- timates, locality of the error, adaptivity
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