6533b7d7fe1ef96bd12682b2
RESEARCH PRODUCT
A fully adaptive wavelet algorithm for parabolic partial differential equations
Jacques LiandratGuillaume Chiavassasubject
FTCS schemeNumerical AnalysisDifferential equationIndependent equationApplied MathematicsMathematical analysisMathematicsofComputing_NUMERICALANALYSISExponential integratorParabolic partial differential equationComputational MathematicsMultigrid methodAlgorithmMathematicsNumerical stabilityNumerical partial differential equationsdescription
We present a fully adaptive numerical scheme for the resolution of parabolic equations. It is based on wavelet approximations of functions and operators. Following the numerical analysis in the case of linear equations, we derive a numerical algorithm essentially based on convolution operators that can be efficiently implemented as soon as a natural condition on the space of approximation is satisfied. The algorithm is extended to semi-linear equations with time dependent (adapted) spaces of approximation. Numerical experiments deal with the heat equation as well as the Burgers equation.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-02-01 | Applied Numerical Mathematics |