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Jung, Chang-Yeol
Analysis and computational methods Lab
Research Interests
  • Analysis, singular perturbations, uncertainty, numerical methods

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Semi-analytic shooting methods for Burgers equation

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Title
Semi-analytic shooting methods for Burgers equation
Author
Gie, Gung-MinJung, Chang-YeolLee, Hoyeon
Issue Date
2023-01
Publisher
Elsevier BV
Citation
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v.418, pp.114694
Abstract
We implement new semi-analytic shooting methods for the stationary viscous Burgers' equation by modifying the classical time differencing methods. When the viscosity is small, a very stiff boundary layer appears and this boundary layer causes significant difficulties to approximate the solution for Burgers' equation. To overcome this issue and improve the numerical quality of the shooting methods with the classical Integrating Factor (IF) methods and Exponential Time Differencing (ETD) methods, we first employ the singular perturbation analysis for Burgers' equation, and derived the so-called correctors that approximate the stiff part of the solution. Then, we build our new semianalytic shooting methods for the stationary viscous Burgers' equation by embedding these correctors into the IF and ETD methods. By performing numerical simulations, we verify that our new schemes, enriched with the correctors, give much better approximations, compared with the classical schemes.(c) 2022 Elsevier B.V. All rights reserved.
URI
https://scholarworks.unist.ac.kr/handle/201301/59892
DOI
10.1016/j.cam.2022.114694
ISSN
0377-0427
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MTH_Journal Papers
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