Wavelets algorithm for the numerical resolution of variable coefficient partial differential equations. (Algorithme à base d’ondelettes pour la résolution numérique d’équations aux dérivées partielles à coefficients variables.) (French. Abridged English version) Zbl 0810.65082

Summary: We present an iterative method to invert variable coefficients operators associated with a \(V\)-elliptic Hermitian form. This method uses the localization properties of orthonormal wavelet bases. It is divided into two steps. The first one provides a first estimate of the inverse; it is built from a smooth approximation obtained using a Galerkin method on a low resolution space and a diagonal correction constructed using small scale wavelets. The second step is an iterative refinement of the first approximation step. Numerical results are presented for operators of the form: \(L = I - (\partial /\partial x)\) \((\nu(x) (\partial/\partial x))\).


65T60 Numerical methods for wavelets
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations