数学
离散小波变换
小波
数学分析
索波列夫空间
搭配(遥感)
搭配法
非线性系统
有界函数
应用数学
偏微分方程
正交配置
边值问题
基函数
小波变换
微分方程
常微分方程
计算机科学
机器学习
物理
量子力学
人工智能
作者
Wei Cai,Jianzhong Wang
摘要
We have designed a cubic spline wavelet-like decomposition for the Sobolev space $H_0^2 (I)$ where I is a bounded interval. Based on a special point value vanishing property of the wavelet basis functions, a fast discrete wavelet transform (DWT) is constructed. This DWT will map discrete samples of a function to its wavelet expansion coefficients in at most $7N\log N$ operations. Using this transform, we propose a collocation method for the initial boundary value problem of nonlinear partial differential equations (PDEs). Then, we test the efficiency of the DWT and apply the collocation method to solve linear and nonlinear PDEs.
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