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Peer-reviewedCC BY-NC-NDJournal of Scientific Computing

Numerical Ergodicity and Optimal Strong Error Estimates for a Class of Novel Tamed Schemes to Superlinear SPDEs

  • Zhihui Liu1
  • Jie Shen2
  1. 1Department of Mathematics & National Center for Applied Mathematics Shenzhen (NCAMS) & Shenzhen International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, People’s Republic of China
  2. 2School of Mathematical Science, Eastern Institute of Technology, Ningbo, 315200, People’s Republic of China
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Abstract

We construct a class of novel tamed schemes for superlinear stochastic partial differential equations (SPDEs), including the stochastic Allen–Cahn equation driven by either multiplicative or additive noise. The schemes preserve the same Lyapunov structure as the original system, and we rigorously establish their longtime unconditional stability. Furthermore, we prove that the corresponding Galerkin-based fully discrete tamed schemes inherit the unique ergodicity of the underlying SPDEs and achieve optimal strong convergence rates in both the multiplicative- and additive-noise cases.

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Cite

BibTeXRIS
BibTeX
@article{liu2026numerical,
  title = {{Numerical Ergodicity and Optimal Strong Error Estimates for a Class of Novel Tamed Schemes to Superlinear SPDEs}},
  author = {Zhihui Liu and Jie Shen},
  journal = {Journal of Scientific Computing},
  year = {2026},
  month = sep,
  doi = {10.1007/s10915-026-03484-5},
  url = {https://doi.org/10.1007/s10915-026-03484-5},
  note = {CC BY-NC-ND},
}
RIS
TY  - JOUR
TI  - Numerical Ergodicity and Optimal Strong Error Estimates for a Class of Novel Tamed Schemes to Superlinear SPDEs
AU  - Zhihui Liu
AU  - Jie Shen
PY  - 2026
DA  - 2026/09/23
JO  - Journal of Scientific Computing
DO  - 10.1007/s10915-026-03484-5
UR  - https://doi.org/10.1007/s10915-026-03484-5
AB  - We construct a class of novel tamed schemes for superlinear stochastic partial differential equations (SPDEs), including the stochastic Allen–Cahn equation driven by either multiplicative or additive noise. The schemes preserve the same Lyapunov structure as the original system, and we rigorously establish their longtime unconditional stability. Furthermore, we prove that the corresponding Galerkin-based fully discrete tamed schemes inherit the unique ergodicity of the underlying SPDEs and achieve optimal strong convergence rates in both the multiplicative- and additive-noise cases.
SN  - 0885-7474
SN  - 1573-7691
ER  -