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Jung, Chang-Yeol
Numerical Analysis Lab.
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Semi-analytic time differencing methods for singularly perturbed initial value problems

Author(s)
Gie, Gung-MinJung, Chang-YeolLee, Hoyeon
Issued Date
2022-09
DOI
10.1002/num.22839
URI
https://scholarworks.unist.ac.kr/handle/201301/54071
Fulltext
https://onlinelibrary.wiley.com/doi/10.1002/num.22839
Citation
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, v.38, no.5, pp.1367 - 1395
Abstract
We implement our new semi-analytic time differencing methods, applied to singularly perturbed non-linear initial value problems. It is well-known that, concerning the singularly perturbed initial problem, a very stiff layer, called initial layer, appears when the perturbation parameter is small, and this stiff initial layer causes significant difficulties to approximate the solution. To improve numerical quality of the classical integrating factor (IF) methods and exponential time differencing (ETD) methods for stiff problems, we first derived the so-called correctors, which are analytic approximations of the stiff part of the solution. Then, by embedding these correctors into the IF and ETD methods, we build our new enriched schemes to improve the IF Runge-Kutta and ETD Runge-Kutta schemes. By performing numerical simulations, we verify that our new enriched schemes give much better approximations of solutions to the stiff problems, compared with the classical schemes without using the correctors.
Publisher
John Wiley & Sons Inc.
ISSN
0749-159X
Keyword (Author)
boundary layersinitial layersnonlinear ordinary differential equationssemi-analytical time differencingsingular perturbation analysisstiff problems
Keyword
DIFFUSION-EQUATIONS

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