Arbitrarily High-Order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen–Cahn Equations
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-021-01746-y
Abstract: We develop and analyze a class of maximum bound preserving schemes for approximately solving Allen–Cahn equations. We apply a k th-order single-step scheme in time (where the nonlinear term is linearized by multi-step extrapolation), and… read more here.
Keywords: order; arbitrarily high; preserving schemes; bound preserving ... See more keywords
The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations
Sign Up to like & getrecommendations! Published in 2018 at "IMA Journal of Numerical Analysis"
DOI: 10.1093/imanum/dry047
Abstract: In this paper we focus on the analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations. A novel energy-preserving scheme is developed based on the discrete gradient method and the Duhamel principle. The local… read more here.
Keywords: schemes solving; energy; preserving schemes; energy preserving ... See more keywords