News & Events
Speaker: Liao Honglin, Professor, School of Mathematics, Nanjing University of Aeronautics and Astronautics
Date: October 22, 2023
Location: B924, Zhixin Building, Central Campus
Sponsor: School of Mathematics, Shandong University
The third-order BDF (BDF3) scheme with variable steps is practically useful in time adaptive simulations for nonlinear gradient flows, hyperbolic systems with multiscale relaxation and stiff kinetic equations. We prove that the BDF3 scheme is stable for non-stiff problems if the adjacent step ratios are less than 2.553, and is stable for linear diffusion equations if the adjacent step ratios are less than 1.4877. Numerical tests show that the variable-step BDF3 method is mesh-robust with a desired convergence rate, even if many of step-ratios are much greater than our theoretical limits, Up to now, the theoretical analysis remains incomplete so far, and mysterious to us.
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