2024-03-29T12:36:04Z
https://tsukuba.repo.nii.ac.jp/oai
oai:tsukuba.repo.nii.ac.jp:00052412
2022-04-27T09:25:54Z
152:1451
152:5654
3:62:5592:2037
Rigorous numerical computations for 1D advection equations with variable coefficients
高安, 亮紀
タカヤス, アキトシ
TAKAYASU, Akitoshi
遠藤, 靖典
エンドウ, ヤスノリ
ENDO, Yasunori
Yoon, Suro
© The JJIAM Publishing Committee and Springer 2011 The original publication is available at www.springerlink.com
This paper provides a methodology of verified computing for solutions to 1D advection equations with variable coefficients. The advection equation is typical partial differential equations (PDEs) of hyperbolic type. There are few results of verified numerical computations to initial-boundary value problems of hyperbolic PDEs. Our methodology is based on the spectral method and semigroup theory. The provided method in this paper is regarded as an efficient application of semigroup theory in a sequence space associated with the Fourier series of unknown functions. This is a foundational approach of verified numerical computations for hyperbolic PDEs. Numerical examples show that the rigorous error estimate showing the well-posedness of the exact solution is given with high accuracy and high speed.
Springer
2019-07
eng
journal article
http://hdl.handle.net/2241/00157834
https://tsukuba.repo.nii.ac.jp/records/52412
10.1007/s13160-019-00345-7
0916-7005
AA10799861
Japan Journal of Industrial and Applied Mathematics
36
2
357
384
https://tsukuba.repo.nii.ac.jp/record/52412/files/JJIAM_36-2.pdf
application/pdf
534.0 kB
2020-07-01