Lazaar, Saiida; Liandrat, Jacques; Tchamitchian, Philippe 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 C. R. Acad. Sci., Paris, Sér. I 319, No. 10, 1101-1107 (1994). 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: \(L = I - (\partial /\partial x)\) \((\nu(x) (\partial/\partial x))\). Cited in 5 Documents MSC: 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 Keywords:numerical results; iterative method; \(V\)-elliptic Hermitian form; orthonormal wavelet bases; Galerkin method; iterative refinement PDFBibTeX XMLCite \textit{S. Lazaar} et al., C. R. Acad. Sci., Paris, Sér. I 319, No. 10, 1101--1107 (1994; Zbl 0810.65082)