Automodeļu diferenciālvienādojumu robežproblēmu iegūšana un to atrisinājumu izturēšanās
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Latvijas Universitāte
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Maģistra darbs veltīts dažu automodeļu diferenciālvienādojumu robežproblēmu iegūšanai un pamatā to skaitliskai izpētei. Darbā pirmajā nodaļā tiek iegūtas un skaitliski risinātas robežproblēmas Blaziusa un Foknera-Skeinas vienādojumiem, kuri rodas pārveidojot Navjē-Stoksa diferenciālvienādojumu sistēmu, kas apraksta viskoza šķidruma plūsmu gar pusbezgalīgu plāksni Blaziusa vienādojuma gadījumā, vai gar ķīli Foknera-Skeinas vienādojuma gadījumā. Darba otrajā nodaļā tiek apskatīts dabiskās siltuma konvekcijas uzdevums ap porainā vidē vertikāli ievietotu sakarsētu plāksni. Tiek iegūta un skaitliski risināta attiecīgā robežproblēma Foknera-Skeinas tipa vienādojumam un apskatīta atrisinājuma atkarība no vienādojumā ietilpstošā parametra vērtībām. Otrā nodaļa satur arī nelielu robežproblēmas kvalitatīvās izpētes sadaļu.
Master thesis Obtaining of self-similar boundary value problems and behavior of their solutions is devoted to obtaining and generally to numerical investigation of some boundary value problems of self-similar differential equations. The first chapter considers the numerical solving of boundary value problems of Blasius and Falkner-Skan differential equations. These problems are obtained by modifying Navier-Stocks equations which describe viscous fluid flow over a semi-infinite plate in case of Blasius equation and over a wedge in cases of Falkner-Skan equation. A free convection about a vertical heated plate embedded in a porous medium is considered in the second chapter. The boundary value problem of a Falkner-Skan type equation is obtained and solved numerically. The solution dependence on a parameter is considered. One small section of the second chapter is devoted to the qualitative analysis of a boundary value problem.
Master thesis Obtaining of self-similar boundary value problems and behavior of their solutions is devoted to obtaining and generally to numerical investigation of some boundary value problems of self-similar differential equations. The first chapter considers the numerical solving of boundary value problems of Blasius and Falkner-Skan differential equations. These problems are obtained by modifying Navier-Stocks equations which describe viscous fluid flow over a semi-infinite plate in case of Blasius equation and over a wedge in cases of Falkner-Skan equation. A free convection about a vertical heated plate embedded in a porous medium is considered in the second chapter. The boundary value problem of a Falkner-Skan type equation is obtained and solved numerically. The solution dependence on a parameter is considered. One small section of the second chapter is devoted to the qualitative analysis of a boundary value problem.