Affiliation:
1. College of Information and Electrical Engineering China Agricultural University Beijing China
2. Department of Computer, Control and Management Engineering University of Rome “La Sapienza” Rome Italy
Abstract
AbstractShannon‐Cosine wavelet function possesses almost all excellent characteristics such as interpolation, compact support, and smoothness. As an interpolation wavelet function, it could be applied in fractional partial differential equations effectively. However, when solving engineering problems in a finite interval, the treatment of the boundary is still not smooth enough. So, the Hermite‐Shannon‐Cosine interval wavelet is constructed using the Hermite interpolation function to achieve smoother transitions at the boundary of the interval, thereby reducing boundary effects. Based on this, a method for solving Fractional PDEs is proposed, the method's performance and its processing capability at the interval boundary are verified by taking the Fractional Fokker‐Planck equation and the Time‐Fractional Korteweg‐de Vries equation as examples. Compared with the multi‐scale Faber‐Schauder wavelet collocation method, Point‐Symmetric interval wavelet spectral method, Dynamic interval wavelet spectral method, and so forth, the experimental results show that the method performs better in terms of numerical accuracy and effectiveness.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Shandong Province
Beijing Natural Science Foundation
Subject
Artificial Intelligence,Computational Theory and Mathematics,Theoretical Computer Science,Control and Systems Engineering