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Mathematical Biosciences and Engineering

2017, Volume 14, Issue 1: 237-248. doi: 10.3934/mbe.2017015
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Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion

  • Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
  • Received: 29 October 2015 Accepted: 12 April 2016 Published: 01 February 2017

  • MSC : Primary: 60H15; Secondary: 35R60

  • We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

    Citation: Henryk Leszczyński, Monika Wrzosek. Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 237-248. doi: 10.3934/mbe.2017015

    Related Papers:

  • We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.


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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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