UM
Status即將出版Forthcoming
WEAK N-BEST POAFD FOR SOLVING PARABOLIC EQUATIONS IN REPRODUCING KERNEL HILBERT SPACE
Bai, Hongfang
2022
Source PublicationJournal of Applied Analysis and Computation
ISSN2156-907X
Volume12Issue:4Pages:1650-1671
AbstractThe analytical solutions and numerical ones of parabolic equations in one space variable and the time variable are constructed by weak N-best pre-orthogonal adaptive Fourier decomposition method (weak N-best POAFD) in reproducing kernel Hilbert space (RKHS). To apply weak N-best POAFD, we first choose a dictionary for weak N-best POAFD and implement pre-orthonormalization to all dictionary elements. Then select some parameters by weak N-best maximal selection principle and determine some normalized dictionary elements iteratively. Thus, the analytical solution can be expressed as a linear combination of these determined normalized dictionary elements with a fast convergence rate. Some numerical examples confirm the good accuracy and applicability of the weak N-best POAFD method in solving the partial differential equations.
Keywordparabolic equation reproducing kernel Hilbert space weak N-best maximum selection principle Weak N-best POAFD
DOI10.11948/20220086
URLView the original
Language英語English
Scopus ID2-s2.0-85134033145
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Document TypeJournal article
CollectionUniversity of Macau
AffiliationDepartment of Mathematics, Faculty of Science and Technology, University of Macau, Macau, 999078, China
First Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Bai, Hongfang. WEAK N-BEST POAFD FOR SOLVING PARABOLIC EQUATIONS IN REPRODUCING KERNEL HILBERT SPACE[J]. Journal of Applied Analysis and Computation,2022,12(4):1650-1671.
APA Bai, Hongfang.(2022).WEAK N-BEST POAFD FOR SOLVING PARABOLIC EQUATIONS IN REPRODUCING KERNEL HILBERT SPACE.Journal of Applied Analysis and Computation,12(4),1650-1671.
MLA Bai, Hongfang."WEAK N-BEST POAFD FOR SOLVING PARABOLIC EQUATIONS IN REPRODUCING KERNEL HILBERT SPACE".Journal of Applied Analysis and Computation 12.4(2022):1650-1671.
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