Fast approximation to Poisson integral based on trigonometric periodic multiresolution analysis

Abstract

In this article, a novel fast numerical computational algorithm for Poisson integral is developed by means of periodic trigonometric multiresolution analysis (PTMRA). The approximation formula of Poisson integral is derived. Subsequently, we establish some error estimates of approximation Poisson integral. Finally, several numerical results are given. Comparing with the existing wavelet-based method, the proposed method gives superior results.

§Dedicated to Professor Wei Lin on the occasion of his 70th birthday.

Keywords:

• Harmonic equations
• Poisson integral
• Multiresolution analysis

Keywords:

• Mathematics Subject Classifications 2000: 31A05
• 31A10

Acknowledgement

This work is supported by National Natural Science Foundation of China (10101013).

Notes

§Dedicated to Professor Wei Lin on the occasion of his 70th birthday.