Abstract
We study an approximation scheme for a nonlinear stochastic wave equation in one-dimensional space, driven by a spacetime white noise. The sequence of approximations is obtained by discretisation of the Laplacian operator. We prove L p-convergence to the solution of the equation and determine the rate of convergence. As a corollary, almost sure convergence, uniformly in time and space, is also obtained. Finally, the speed of convergence is tested numerically.
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⋆Supported by the grant BMF 2003-01345 from the Dirección General de Investigación, Ministerio de Ciencia y Tecnología, Spain.
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Quer-Sardanyons, L., Sanz-Solé, M. Space Semi-Discretisations for a Stochastic Wave Equation. Potential Anal 24, 303–332 (2006). https://doi.org/10.1007/s11118-005-9002-0
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DOI: https://doi.org/10.1007/s11118-005-9002-0