论文标题
在高维半椭圆形偏微分方程的数值近似中克服维数的诅咒
Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations
论文作者
论文摘要
最近，已经引入并证明了所谓的全历史递归多层次PICARD（MLP）近似方案，以克服用Lipschitz非线性的半线性抛物线部分微分方程（PDE）的数值近似值的差异。本文的关键贡献是介绍和分析具有Lipschitz非线性的某些半线性椭圆形PDE的MLP近似方案的新变体，并证明所提出的近似方案克服了此类半线性椭圆形PDES数值近似值的维数诅咒。
Recently, so-called full-history recursive multilevel Picard (MLP) approximation schemes have been introduced and shown to overcome the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations (PDEs) with Lipschitz nonlinearities. The key contribution of this article is to introduce and analyze a new variant of MLP approximation schemes for certain semilinear elliptic PDEs with Lipschitz nonlinearities and to prove that the proposed approximation schemes overcome the curse of dimensionality in the numerical approximation of such semilinear elliptic PDEs.
