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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:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L67 Shocks and singularities for hyperbolic equations
35Q72 Other PDE from mechanics (MSC2000)
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35R35 Free boundary problems for PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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