Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion
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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| Format: | Article |
| Language: | English |
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AIMS Press
2017-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017015 |
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| author | Henryk Leszczyński Monika Wrzosek |
| author_facet | Henryk Leszczyński Monika Wrzosek |
| author_sort | Henryk Leszczyński |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-289b7e752b2d493d9c1d288e29b5c01b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-289b7e752b2d493d9c1d288e29b5c01b2025-01-24T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-01-0114123724810.3934/mbe.2017015Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motionHenryk Leszczyński0Monika Wrzosek1Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, PolandInstitute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, PolandWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2017015newton's methodwave equationstochastic differential equationsprobabilistic convergencenonlocal dependence |
| spellingShingle | Henryk Leszczyński Monika Wrzosek Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion Mathematical Biosciences and Engineering newton's method wave equation stochastic differential equations probabilistic convergence nonlocal dependence |
| title | Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion |
| title_full | Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion |
| title_fullStr | Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion |
| title_full_unstemmed | Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion |
| title_short | Newtons method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion |
| title_sort | newtons method for nonlinear stochastic wave equations driven by one dimensional brownian motion |
| topic | newton's method wave equation stochastic differential equations probabilistic convergence nonlocal dependence |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017015 |
| work_keys_str_mv | AT henrykleszczynski newtonsmethodfornonlinearstochasticwaveequationsdrivenbyonedimensionalbrownianmotion AT monikawrzosek newtonsmethodfornonlinearstochasticwaveequationsdrivenbyonedimensionalbrownianmotion |