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The proposed method is shown to be unconditionally stable in spatial dimensions\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$d\\in \\{1,2,3\\}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mo>\u2208<\/mml:mo>\n                            <mml:mo>{<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>3<\/mml:mn>\n                            <mml:mo>}<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . Beyond the inherent challenges caused by, see, e.g., [1], the cubic non-globally Lipschitz drift term and multiplicative driving noise in the convergence analysis, the Milstein scheme further complicates the error estimation of the noise term compared to the Euler-Maruyama discretization. By introducing a novel auxiliary process, we rigorously establish strong convergence rates in both space and time under mild assumptions for\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$d\\in \\{1,2\\}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>d<\/mml:mi>\n                            <mml:mo>\u2208<\/mml:mo>\n                            <mml:mo>{<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mo>}<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . Our analysis shows that the temporal convergence order is doubled compared to that of tamed Euler-Maruyama scheme. Numerical experiments are provided to confirm the theoretical results and to demonstrate that the proposed scheme exhibits improved robustness over the pure semi-implicit Milstein method.\n                  <\/jats:p>","DOI":"10.1007\/s10915-026-03218-7","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T09:35:37Z","timestamp":1771925737000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An Efficient Tamed Milstein Scheme for the Stochastic Allen-Cahn Equation with Multiplicative Noise"],"prefix":"10.1007","volume":"107","author":[{"given":"Xiao","family":"Qi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"George","family":"Dewhirst","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5686-5017","authenticated-orcid":false,"given":"Yubin","family":"Yan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,2,24]]},"reference":[{"key":"3218_CR1","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/s40072-020-00179-2","volume":"9","author":"Z Liu","year":"2021","unstructured":"Liu, Z., Qiao, Z.: Strong approximation of monotone stochastic partial differential equations driven by multiplicative noise. 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If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of Interest"}}],"article-number":"10"}}