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On Wavelet-Galerkin Methods for Semilinear Parabolic Equations with Additive Noise

  • Mihály KovácsEmail author
  • Stig Larsson
  • Karsten Urban
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 65)

Abstract

We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler’s method the equation is split into a linear stochastic equation and a non-linear random evolution equation. The linear stochastic equation is discretized in space by a non-adaptive wavelet-Galerkin method. This equation is solved first and its solution is substituted into the nonlinear random evolution equation, which is solved by an adaptive wavelet method. We provide mean square estimates for the overall error.

Keywords

Additive Noise Stochastic Partial Differential Equation Adaptive Wavelet Unique Mild Solution Stochastic Convolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of OtagoDunedinNew Zealand
  2. 2.Mathematical SciencesChalmers University of TechnologyGothenburgSweden
  3. 3.Institute for Numerical MathematicsUlm UniversityUlmGermany

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