A time-accurate pseudo-wavelet scheme for parabolic and hyperbolic PDE’s. (English) Zbl 1159.65372
Summary: We propose wavelet Taylor-Galerkin schemes for parabolic and hyperbolic PDEs taking full advantage of the compression properties of wavelet basis. The discretization in time is performed before the spatial discretization by introducing high-order generalization of the standard time-stepping schemes with the help of Taylor series expansion in time step. Then, we present numerical results for a convection problem in one dimension and Gaussian translating hill problem in two dimensions. Finally, results for the two-dimensional turbulence are shown.
MSC:
| 65T50 | Numerical methods for discrete and fast Fourier transforms |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35K99 | Parabolic equations and parabolic systems |
| 35L99 | Hyperbolic equations and hyperbolic systems |
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