Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion | Zendy

Henryk Leszczyński | Zendy; Monika Wrzosek | Zendy

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Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion

Author(s) -

Henryk Leszczyński,

Monika Wrzosek

Publication year - 2016

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2017015

Subject(s) - nonlinear system , brownian motion , mathematics , white noise , convergence (economics) , probabilistic logic , newton's method , motion (physics) , mathematical analysis , noise (video) , sense (electronics) , classical mechanics , computer science , physics , statistics , quantum mechanics , artificial intelligence , economics , image (mathematics) , economic growth , engineering , electrical engineering

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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