A wavelet based numerical method for nonlinear partial differential equations
Stephan Dahlke, Mathias Lindemann, Gerd Teschke, M. Zhariy, Maria Joana Soares, Paula Cerejeiras, Uwe Kähler · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2003
The purpose of this paper is to present a wavelet–Galerkin scheme for solving nonlinear elliptic partial differential equations. We select as trial spaces a nested sequence of spaces from an appropriate biorthogonal multiscale analysis. This gives rise to a nonlinear discretized system. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets to obtain knot oriented quadrature rules. Finally, Newton’s method is applied to approximate the solution in the given ansatz space. The results of some numerical experiments with different biorthogonal systems, confirming the applicability of our scheme, are presented.