A simplified Milstein scheme for SPDEs with multiplicative noise
Summary: This paper deals with a research question raised by \textit{A. Jentzen} and \textit{M. Röckner} [Found. Comput. Math. 15, No. 2, 313--362 (2015; Zbl 1318.60072)], whether the exponential term in their introduced scheme can be replaced by a simpler mollifier. This replacement can lead to more simplification and computational reduction in simulation. So, in this paper, we essentially replace the exponential term with a Padé approximation of order 1 and denote the resulting scheme by simplified Milstein scheme. The convergence analysis for this scheme is carried out and it is shown that even with this replacement the order of convergence is maintained, while the resulting scheme is easier to implement and slightly more efficient computationally. Some numerical tests are given that confirm the order of accuracy and also computational cost reduction.
scientific article; zbMATH DE number 7021796
scientific article