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A wavelet based space-time adaptive numerical method for partial differential equations. (English) Zbl 0768.65062

A space-time adaptive algorithm based on wavelet orthonormal bases is described for solving the heat equation, the linear advection equation and the one-dimensional Burgers equation. The stability of this algorithm is studied. Numerical results are presented.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35Q53 KdV equations (Korteweg-de Vries equations)
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References:

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