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

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Monte Carlo and Quasi-Monte Carlo Methods 2012

Part of the book series: Springer Proceedings in Mathematics & Statistics ((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.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Otago, 56, Dunedin, New Zealand

    Mihály Kovács

  2. Mathematical Sciences, Chalmers University of Technology, SE–412 96, Gothenburg, Sweden

    Stig Larsson

  3. Institute for Numerical Mathematics, Ulm University, Helmholtzstr. 18, DE–89069, Ulm, Germany

    Karsten Urban

Authors
  1. Mihály Kovács
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  2. Stig Larsson
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  3. Karsten Urban
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Corresponding author

Correspondence to Mihály Kovács .

Editor information

Editors and Affiliations

  1. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Josef Dick

  2. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Frances Y. Kuo

  3. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Gareth W. Peters

  4. The University of New South Wales School of Mathematics and Statistics, Sydney, New South Wales, Australia

    Ian H. Sloan

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Kovács, M., Larsson, S., Urban, K. (2013). On Wavelet-Galerkin Methods for Semilinear Parabolic Equations with Additive Noise. In: Dick, J., Kuo, F., Peters, G., Sloan, I. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2012. Springer Proceedings in Mathematics & Statistics, vol 65. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41095-6_24

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