Non-Equidistant Numerical Methods for Ordinary Differential Equation with Periodical Boundary Value

Xin Cai

doi:10.4028/www.scientific.net/KEM.467-469.383

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HomeKey Engineering MaterialsKey Engineering Materials Vols. 467-469Non-Equidistant Numerical Methods for Ordinary...

Non-Equidistant Numerical Methods for Ordinary Differential Equation with Periodical Boundary Value

Abstract:

Ordinary differential equation with periodical boundary value and small parameter multiplied in the highest derivative was considered. The solution of the problem has boundary layers, which is thin region in the neighborhood of the boundary of the domain. Firstly, the properties of boundary layer were discussed. The solution was decomposed into the smooth component and the singular component. The derivatives of the smooth component and the singular component were estimated. Secondly, mesh partition techniques were presented according to one transition point method and multi-transition points method. Thirdly numerical methods based on non-equidistant mesh partition were presented to solve the problem. Finally error estimations were given for both computational methods.

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Periodical:

Key Engineering Materials (Volumes 467-469)

Pages:

383-388

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.467-469.383

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Online since:

February 2011

Authors:

Xin Cai

Keywords:

Non-Equidistant, Numerical Method, Periodical

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References

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