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A dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain. (English) Zbl 0847.65073
Authors’ summary: A dynamically adaptive multilevel wavelet collocation method is developed for the solution of partial differential equations. The multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution. High solution computations are performed only in regions where sharp transitions occur. The scheme handles general boundary conditions. The method is applied to the solution of the one-dimensional Burgers equation with small viscosity, a moving shock problem, and a nonlinear thermoacoustic wave problem. The results indicate that the method is very accurate and efficient.

MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35L67Shocks and singularities
35Q72Other PDE from mechanics (MSC2000)
65M55Multigrid methods; domain decomposition (IVP of PDE)
35R35Free boundary problems for PDE
35Q53KdV-like (Korteweg-de Vries) equations
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