Sharp L2 Norm Convergence of Variable-Step BDF2 Implicit Scheme for the Extended Fisher–Kolmogorov Equation
A variable-step BDF2 time-stepping method is investigated for simulating the extended Fisher-Kolmogorov equation. The time-stepping scheme is shown to preserve a discrete energy dissipation law if the adjacent time-step ratios rn≔Τn/Τn−1<3+17/2≈3.561. With the aid of discrete orthogonal convoluti...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2023/1869660 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850174182686457856 |
|---|---|
| author | Yang Li Qihang Sun Naidan Feng Jianjun Liu |
| author_facet | Yang Li Qihang Sun Naidan Feng Jianjun Liu |
| author_sort | Yang Li |
| collection | DOAJ |
| description | A variable-step BDF2 time-stepping method is investigated for simulating the extended Fisher-Kolmogorov equation. The time-stepping scheme is shown to preserve a discrete energy dissipation law if the adjacent time-step ratios rn≔Τn/Τn−1<3+17/2≈3.561. With the aid of discrete orthogonal convolution kernels, concise L2 norm error estimates are proved, for the first time, under the mild step ratios constraint 0<rn<3.561. Our error estimates are almost independent of the step ratios rn so that the proposed numerical scheme is robust with respect to the variations of time steps. An adaptive time-stepping strategy based on solution accuracy is then applied to update the computational efficiency. Numerical examples are included to illustrate our theoretical results. |
| format | Article |
| id | doaj-art-c8b91e75389d4e5796bdb77e5b51fbeb |
| institution | OA Journals |
| issn | 2314-8888 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-c8b91e75389d4e5796bdb77e5b51fbeb2025-08-20T02:19:41ZengWileyJournal of Function Spaces2314-88882023-01-01202310.1155/2023/1869660Sharp L2 Norm Convergence of Variable-Step BDF2 Implicit Scheme for the Extended Fisher–Kolmogorov EquationYang Li0Qihang Sun1Naidan Feng2Jianjun Liu3College of Computer Science and EngineeringDepartment of MathematicsCollege of Computer Science and EngineeringCollege of Computer Science and EngineeringA variable-step BDF2 time-stepping method is investigated for simulating the extended Fisher-Kolmogorov equation. The time-stepping scheme is shown to preserve a discrete energy dissipation law if the adjacent time-step ratios rn≔Τn/Τn−1<3+17/2≈3.561. With the aid of discrete orthogonal convolution kernels, concise L2 norm error estimates are proved, for the first time, under the mild step ratios constraint 0<rn<3.561. Our error estimates are almost independent of the step ratios rn so that the proposed numerical scheme is robust with respect to the variations of time steps. An adaptive time-stepping strategy based on solution accuracy is then applied to update the computational efficiency. Numerical examples are included to illustrate our theoretical results.http://dx.doi.org/10.1155/2023/1869660 |
| spellingShingle | Yang Li Qihang Sun Naidan Feng Jianjun Liu Sharp L2 Norm Convergence of Variable-Step BDF2 Implicit Scheme for the Extended Fisher–Kolmogorov Equation Journal of Function Spaces |
| title | Sharp L2 Norm Convergence of Variable-Step BDF2 Implicit Scheme for the Extended Fisher–Kolmogorov Equation |
| title_full | Sharp L2 Norm Convergence of Variable-Step BDF2 Implicit Scheme for the Extended Fisher–Kolmogorov Equation |
| title_fullStr | Sharp L2 Norm Convergence of Variable-Step BDF2 Implicit Scheme for the Extended Fisher–Kolmogorov Equation |
| title_full_unstemmed | Sharp L2 Norm Convergence of Variable-Step BDF2 Implicit Scheme for the Extended Fisher–Kolmogorov Equation |
| title_short | Sharp L2 Norm Convergence of Variable-Step BDF2 Implicit Scheme for the Extended Fisher–Kolmogorov Equation |
| title_sort | sharp l2 norm convergence of variable step bdf2 implicit scheme for the extended fisher kolmogorov equation |
| url | http://dx.doi.org/10.1155/2023/1869660 |
| work_keys_str_mv | AT yangli sharpl2normconvergenceofvariablestepbdf2implicitschemefortheextendedfisherkolmogorovequation AT qihangsun sharpl2normconvergenceofvariablestepbdf2implicitschemefortheextendedfisherkolmogorovequation AT naidanfeng sharpl2normconvergenceofvariablestepbdf2implicitschemefortheextendedfisherkolmogorovequation AT jianjunliu sharpl2normconvergenceofvariablestepbdf2implicitschemefortheextendedfisherkolmogorovequation |