Wavelets and the numerical solution of boundary value problems

AbstractWe present a new numerical method for the solution of partial differential equations in nonseparable domains. The method uses a Wavelet-Galerkin solver with a nontrivial adaptation of the standard capacitance matrix method. The numerical solutions exhibit spectral convergence with regard to the order of the compactly-supported, Daubechies wavelet basis. Furthermore, the rate of convergence is found to be independent of the geometry. We solve the Helmholtz equation since, for the indefinite case, the solutions have qualitative properties that well illustrate the applications of our method