Work

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

Year: 2026

Type: article

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.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-026-03484-5

Authors: Zhihui Liu, Jie Shen

Institutions: Southern University of Science and Technology, Eastern Institute of Technology, Ningbo

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province