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Linearly stabilized schemes for the time integration of stiff nonlinear PDEs

Resource type
Thesis type
(Thesis) M.Sc.
Date created
2016-12-09
Authors/Contributors
Abstract
In many applications, the governing PDE to be solved numerically will contain a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by stability restrictions is preferred. On the other hand, if the stiff component is nonlinear, the complexity and cost per step of using an implicit method is heightened, and explicit methods may be preferred for their simplicity and ease of implementation. In this thesis, we analyze new and existing linearly stabilized schemes for the purpose of integrating stiff nonlinear PDEs in time. These schemes compute the nonlinear term explicitly and, at the cost of solving a linear system with a matrix that is fixed throughout, are unconditionally stable, thus combining the advantages of explicit and implicit methods. Applications are presented to illustrate the use of these methods.
Document
Identifier
etd9887
Copyright statement
Copyright is held by the author.
Permissions
This thesis may be printed or downloaded for non-commercial research and scholarly purposes.
Scholarly level
Supervisor or Senior Supervisor
Thesis advisor: Ruuth, Steve
Member of collection
Download file Size
etd9887_KChow.pdf 3.85 MB

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