High Order Semi-implicit Multistep Methods for Time-Dependent Partial Differential Equations
Giacomo Albi , Lorenzo Pareschi
Communications on Applied Mathematics and Computation ›› 2021, Vol. 3 ›› Issue (4) : 701 -718.
High Order Semi-implicit Multistep Methods for Time-Dependent Partial Differential Equations
We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in Boscarino et al. (J. Sci. Comput. 68: 975–1001, 2016) for Runge-Kutta methods, these semi-implicit techniques give a great flexibility, and allow, in many cases, the construction of simple linearly implicit schemes with no need of iterative solvers. In this work, we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype linear advection-diffusion equation and in the setting of strong stability preserving (SSP) methods. Our findings are demonstrated on several examples, including nonlinear reaction-diffusion and convection-diffusion problems.
Innovative numerical methods for evolutionary partial differential equations and applications(PRIN 2017 No. 2017KKJP4X)
Università degli Studi di Verona
/
| 〈 |
|
〉 |
PDF
