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Comparison of explicit and implicit difference methods for quasilinear functional differential equations

W. Czernous, Z. Kamont (2011)

Applicationes Mathematicae

We give a theorem on error estimates of approximate solutions for explicit and implicit difference functional equations with unknown functions of several variables. We apply this general result to investigate the stability of difference methods for quasilinear functional differential equations with initial boundary condition of Dirichlet type. We consider first order partial functional differential equations and parabolic functional differential problems. We compare the properties of explicit...

Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes

Dana Kotorová (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this work we describe two schemes for solving level set equation in 3D with a method based on finite volumes. These schemes use the so-called dual volumes as in [Coudiére, Y., Hubert, F.: A 3D discrete duality finite volume method for nonlinear elliptic equations Algoritmy 2009 (2009), 51–60.], [Hermeline, F.: A finite volume method for approximating 3D diffusion operators on general meshes Journal of Computational Physics 228, 16 (2009), 5763–5786.], where they are used for the nonlinear elliptic...

Comparison principle for a nonlinear parabolic problem of a nonmonotone type

Tomas Vejchodský (2002)

Applicationes Mathematicae

A nonlinear parabolic problem with the Newton boundary conditions and its weak formulation are examined. The problem describes nonstationary heat conduction in inhomogeneous and anisotropic media. We prove a comparison principle which guarantees that for greater data we obtain, in general, greater weak solutions. A new strategy of proving the comparison principle is presented.

Comparison theorems for temperatures in noncylindrical domains

Eugene B. Fabes, Nicola Garofalo, Sandro Salsa (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota gli autori presentano alcuni risultati riguardanti il comportamento alla frontiera di domini non cilindrici delle soluzioni positive dell'equazione del calore. Una conseguenza è che due soluzioni positive qualunque, che si annullano su una parte della frontiera laterale, tendono a zero con lo stesso ordine.

Competition of Species with Intra-Specific Competition

N. Apreutesei, A. Ducrot, V. Volpert (2008)

Mathematical Modelling of Natural Phenomena

Intra-specific competition in population dynamics can be described by integro-differential equations where the integral term corresponds to nonlocal consumption of resources by individuals of the same population. Already the single integro-differential equation can show the emergence of nonhomogeneous in space stationary structures and can be used to model the process of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom....

Compétition Réaction-Diffusion et comportement asymptotique d’un problème d’obstacle doublement non linéaire

Fahd Karami (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Le but de cet article est l’étude de la compétition Réaction-Diffusion pour un problème de type β ( w ) t - d ε div a ( x , D w ) + r ε g x , β ( w ) = f , où a est un opérateur de Lerray-Lions, β est une fonction continue croissante et la réaction g est une fonction croissante qui dépend de l’espace x . On suppose que les coefficients de diffusion d ε et de Réaction r ε dépendent du paramètre ε avec d ε et/ou r ε tends vers + ∞ lorsque ε → 0 . Dans le cas où, le coefficient de réaction est très rapide, nous étudions le comportement asymptotique lorsque t → ∞ de la solution...

Computation of bifurcated branches in a free boundary problem arising in combustion theory

Olivier Baconneau, Claude-Michel Brauner, Alessandra Lunardi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a parabolic 2D Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter u * does not exceed a critical value u * c . The latter is the limit of a decreasing sequence ( u * k ) of bifurcation points. The paper deals with the study of the 2D bifurcated branches from the planar branch, for small k. Our technique is based on the elimination of the unknown front, turning the problem into a fully nonlinear...

Computational design optimization of low-energy buildings

Vala, Jiří (2017)

Proceedings of Equadiff 14

European directives and related national technical standards force the substantial reduction of energy consumption of all types of buildings. This can be done thanks to the massive insulation and the improvement of quality of building enclosures, using the simple evaluation assuming the one-dimensional stationary heat conduction. However, recent applications of advanced materials, structures and technologies force the proper physical, mathematical and computational analysis coming from the thermodynamic...

Computational modelling of thermal consumption of buildings with controlled interior temperature

Vala, Jiří (2017)

Programs and Algorithms of Numerical Mathematics

New materials, structures and technologies used in civil engineering impeach traditional evaluations of the annual thermal consumption of buildings, based on the quasi-stationary estimate of the thermal resistance of the building envelope, or some operational parts of such building with the guaranteed temperature. The complete proper physical analysis, applying the principles of thermodynamics and appropriate constitutive relations for particular material layers and air in rooms, is not realistic...

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