WEAK N-BEST POAFD FOR SOLVING PARABOLIC EQUATIONS IN REPRODUCING KERNEL HILBERT SPACE

Hongfang Bai

doi:10.11948/20220086

2022 Volume 12 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(4): 1650-1671

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Hongfang Bai. WEAK N-BEST POAFD FOR SOLVING PARABOLIC EQUATIONS IN REPRODUCING KERNEL HILBERT SPACE[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1650-1671. doi: 10.11948/20220086

Citation:

Hongfang Bai. WEAK N-BEST POAFD FOR SOLVING PARABOLIC EQUATIONS IN REPRODUCING KERNEL HILBERT SPACE[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1650-1671. doi: 10.11948/20220086

WEAK N-BEST POAFD FOR SOLVING PARABOLIC EQUATIONS IN REPRODUCING KERNEL HILBERT SPACE

Hongfang Bai^1, ,

1.
Department of Mathematics, Faculty of Science and Technology, University of Macau, 999078 Macau, China

Corresponding author: Email address: byebyenever@163.com (H. F. Bai)

Abstract

Abstract

The 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.
- Weak N-best POAFD /
- weak N-best maximum selection principle /
- parabolic equation /
- reproducing kernel Hilbert space
MSC: 42A16, 41A30, 65M32, 35A35

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References

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