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math.NA2024
A mean correction for improved phase-averaging accuracy in oscillatory, multiscale, differential equations
Timothy C. Andrews, Beth A. Wingate
This paper introduces a new algorithm to improve the accuracy of numerical phase-averaging in oscillatory, multiscale, differential equations. Phase-averaging is a timestepping met…
math.NA2024
The effect of linear dispersive errors on nonlinear timestepping accuracy in the f-plane rotating shallow water equations
Timothy C. Andrews, Jemma Shipton, Beth A. Wingate
For simulations of time evolution problems, such as weather and climate models, taking the largest stable timestep is advantageous for reducing wall-clock time. A drawback of doing…