A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit in local and stabilizing terms in the underlying PDE and explicit in nonlocal and unstabilizing terms. Unconditional stability and convergence of the numerical scheme are proven by the energy method and by algebraic techniques. This stability result is surprising because usually when different methods are combined, the stability properties of the least stable method plays a determining role in the combination.
Mean-square stability and error analysis of implicit time-stepping schemes for linear parabolic SPDEs with multiplicative Wiener noise in the first derivative
Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation
Columbia University（哥伦比亚大学）；University of South Carolina（南卡罗来纳大学）；Beijing Computational Science Research Center（北京计算科学研究中心）；The Hong Kong Polytechnic University（香港理工大学）
Stability and convergence analysis of unconditionally original energy dissipative implicit-explicit Runge--Kutta methods for the phase field crystal models without Lipschitz assumptions
School of Mathematics and State Key Laboratory of Cryptography and Digital Economy Security, Shandong University（山东大学数学学院和密码与数字经济安全国家重点实验室）；School of Mathematics, Shandong University（山东大学数学学院）；Department of Mathematics, SUSTech International Center for Mathematics & National Center for Applied Mathematics Shenzhen (NCAMS), Guangdong Provincial Key Laboratory of Computational Science and Material Design, Southern University of Science and Technology（南方科技大学数学系、南方科技大学国际数学中心与应用数学深圳国家研究中心（NCAMS）、广东省计算科学与材料设计重点实验室）
