ADAPTIVE WAVELET COLLOCATION METHODS FOR INITIAL VALUE BOUNDARY PROBLEMS OF NONLINEAR PDE''S
Wei Cai, Jianzhong Wang · Defense Technical Information Center (DTIC) · 1993
We have designed a cubic spline wavelet decomposition for the Sobolev space HO(2)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's. Wavelet