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Newton's 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

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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Keywords Newton's method; wave equation; stochastic differential equations; probabilistic convergence; nonlocal dependence

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

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