Second-generation wavelet collocation method for the solution of partial differential equations

@article{Vasilyev2000SecondgenerationWC,
  title={Second-generation wavelet collocation method for the solution of partial differential equations},
  author={Oleg V. Vasilyev and Christopher Bowman},
  journal={Journal of Computational Physics},
  year={2000},
  volume={165},
  pages={660-693}
}
An adaptive numerical method for solving partial differential equations is developed. The method is based on the whole new class of second-generation wavelets. Wavelet decomposition is used for grid adaptation and interpolation, while a new O(N) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The treatment of nonlinear terms and general boundary conditions is a straightforward task due to the collocation… 

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