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Pseudospectral methods for a class o...

Geldhof, Sam.

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Pseudospectral methods for a class of evolutionary systems.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Pseudospectral methods for a class of evolutionary systems./
作者:	Geldhof, Sam.
面頁冊數:	83 p.
附註:	Source: Masters Abstracts International, Volume: 51-05.
Contained By:	Masters Abstracts International51-05(E).
標題:	Applied Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1535600
ISBN:	9781303017407

Pseudospectral methods for a class of evolutionary systems.
Geldhof, Sam.

Pseudospectral methods for a class of evolutionary systems. - 83 p.

Source: Masters Abstracts International, Volume: 51-05.

Thesis (M.S.)--Colorado School of Mines, 2013.

Mathematical and computer modeling of various physical processes typically involve evolutionary systems which are a class of time dependent partial differential equations. Exact solutions to many of these evolutionary systems are not known in general and a variety of numerical methods have been proposed to simulate the solutions of these problems. In this thesis, we approximate the solution of evolutionary systems using the method of lines in which we separately discretize our problem in space and in time. The spatial discretization is done using a class of high order Fourier spectral Galerkin methods with quadrature, also known as Fourier pseudospectral methods. Many evolutionary systems that we will be concerned with contain quadratic nonlinear terms, causing aliasing affects. We consider two techniques to resolve the affects of aliasing. The spatial discretization reduces the problem to a system of ordinary differential equations in time which we solve using standard numerical techniques. Many of these systems are stiff and therefore we also consider the stability of our numerical solvers and consider some implicit methods. In order to obtain accurate solutions for many problems, we must calculate a large number of Fourier coefficients, leading to impractical computation times. Therefore, we seek methods that allow us to calculate more Fourier modes in a computationally inexpensive manner. The algorithms developed and implemented in this thesis are based on the high order pseudospectral Galerkin method with quadrature in space and various implicit and explicit discretization techniques in time..

ISBN: 9781303017407Subjects--Topical Terms:

1669109
Applied Mathematics.

Pseudospectral methods for a class of evolutionary systems.
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502 $a Thesis (M.S.)--Colorado School of Mines, 2013.
520 $a Mathematical and computer modeling of various physical processes typically involve evolutionary systems which are a class of time dependent partial differential equations. Exact solutions to many of these evolutionary systems are not known in general and a variety of numerical methods have been proposed to simulate the solutions of these problems. In this thesis, we approximate the solution of evolutionary systems using the method of lines in which we separately discretize our problem in space and in time. The spatial discretization is done using a class of high order Fourier spectral Galerkin methods with quadrature, also known as Fourier pseudospectral methods. Many evolutionary systems that we will be concerned with contain quadratic nonlinear terms, causing aliasing affects. We consider two techniques to resolve the affects of aliasing. The spatial discretization reduces the problem to a system of ordinary differential equations in time which we solve using standard numerical techniques. Many of these systems are stiff and therefore we also consider the stability of our numerical solvers and consider some implicit methods. In order to obtain accurate solutions for many problems, we must calculate a large number of Fourier coefficients, leading to impractical computation times. Therefore, we seek methods that allow us to calculate more Fourier modes in a computationally inexpensive manner. The algorithms developed and implemented in this thesis are based on the high order pseudospectral Galerkin method with quadrature in space and various implicit and explicit discretization techniques in time..
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