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Newton's method for stochastic semilinear wave equations driven by multiplicative time‐space noise

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  • Henryk Leszczyński
  • Monika Wrzosek

Abstract

Semilinear wave equations with additive or one‐dimensional noise are treatable by various iterative and numerical methods. We study more difficult models of semilinear wave equations with infinite dimensional multiplicative spatially correlated noise. Our proof of probabilistic second‐order convergence of some iterative methods is based on Da Prato and Zabczyk's maximal inequalities.

Suggested Citation

  • Henryk Leszczyński & Monika Wrzosek, 2023. "Newton's method for stochastic semilinear wave equations driven by multiplicative time‐space noise," Mathematische Nachrichten, Wiley Blackwell, vol. 296(2), pages 689-700, February.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:2:p:689-700
    DOI: 10.1002/mana.202000467
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