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| ANNOUNCEMENT ON “SHARP ERROR ESTIMATE OF BDF2 SCHEME WITH VARIABLE TIME STEPS FOR LINEAR REACTION-DIFFUSION EQUATIONS” |
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ZHANG Ji-wei1, ZHAO Cheng-chao2
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1.School of Mathematics and Statistics, Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China;2.Beijing Computational Science Research Center, Beijing 100193, China
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| 摘要: |
| In this note we announce the sharp error estimate of BDF2 scheme for linear diffusion reaction problem with variable time steps. Our analysis shows that the optimal second-order convergence does not require the high-order methods or the very small time steps τ1=O(τ2) for the first level solution u1. This is, the first-order consistence of the first level solution u1 like BDF1 (i.e. Euler scheme) as a starting point does not cause the loss of global temporal accuracy, and the ratios are updated to rk ≤ 4.8645. |
| 关键词: BDF2 DOC DCC variable time-steps sharp error estimate |
| DOI： |
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| 基金项目:Supported by Natural Science Foundation of Hubei Province(2019CFA007); Supported by NSFC (11771035). |
|
| ANNOUNCEMENT ON “SHARP ERROR ESTIMATE OF BDF2 SCHEME WITH VARIABLE TIME STEPS FOR LINEAR REACTION-DIFFUSION EQUATIONS” |
|
ZHANG Ji-wei1, ZHAO Cheng-chao2
|
|
1.School of Mathematics and Statistics, Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China;2.Beijing Computational Science Research Center, Beijing 100193, China
|
| Abstract: |
| In this note we announce the sharp error estimate of BDF2 scheme for linear diffusion reaction problem with variable time steps. Our analysis shows that the optimal second-order convergence does not require the high-order methods or the very small time steps τ1=O(τ2) for the first level solution u1. This is, the first-order consistence of the first level solution u1 like BDF1 (i.e. Euler scheme) as a starting point does not cause the loss of global temporal accuracy, and the ratios are updated to rk ≤ 4.8645. |
| Key words: BDF2 DOC DCC variable time-steps sharp error estimate |
