Open AccessNewton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion
Author(s) -
Henryk Leszczyński,
Monika Wrzosek
Publication year - 2017
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.