Grid stabilization for the one-dimensional advection equation using biased finite differnces of odd orders and orders higher than twenty-two

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dc.contributor.author Whitley, Michael Aaron
dc.date.accessioned 2013-08-16T18:52:08Z
dc.date.available 2013-08-16T18:52:08Z
dc.date.issued 2013-08-16
dc.identifier.uri http://hdl.handle.net/2097/16285
dc.description.abstract This work utilizes finite differences to approximate the first derivative of non-periodic smooth functions. Math literature indicates that stabilizing Partial Differential Equation solvers based on high order finite difference approximations of spatial derivatives of a non-periodic function becomes problematic near a boundary. Hagstrom and Hagstrom have discovered a method of introducing additional grid points near a boundary, which has proven to be effective in stabilizing Partial Differential Equation solvers. Hagstrom and Hagstrom demonstrated their method for the case of the one-dimensional advection equation using spatial derivative approximations of even orders up to twenty-second order. In this dissertation, we explore the efficacy of the Hagstrom and Hagstrom method for the same Partial Differential Equation with spatial derivative approximations of odd orders and orders higher than twenty-two and report the number and locations of additional grid points required for stability in each case. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Finite difference en_US
dc.subject Stable boundary en_US
dc.subject Advection en_US
dc.subject Equation en_US
dc.title Grid stabilization for the one-dimensional advection equation using biased finite differnces of odd orders and orders higher than twenty-two en_US
dc.type Thesis en_US
dc.description.degree Master of Science en_US
dc.description.level Masters en_US
dc.description.department Department of Mathematics en_US
dc.description.advisor Nathan Albin en_US
dc.subject.umi Mathematics (0405) en_US
dc.date.published 2013 en_US
dc.date.graduationmonth August en_US


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