.png){kind=icon}
.png){kind=icon}
Return
LINEARLY IMPLICIT MULTISTEP METHODS FOR TIME INTEGRATION
.png){kind=icon}
OA
AI
DOI：10.1137/20M133748X.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Time integration methods for solving initial value problems are an important com-ponent of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, which significantly relax restrictions on timestep size. However, implicit methods require solutions to one or more systems of nonlinear equations at each timestep, which for large simulations can be prohibitively expensive. This paper introduces a new family of linearly im-plicit multistep methods (LIMM), which only requires the solution of one linear system per timestep. Order conditions and stability theory for these methods are presented, as well as design and im-plementation considerations. Practical methods of order up to five are developed that have similar error coefficients, but improved stability regions, when compared to the widely used BDF methods. Numerical testing of a self-starting variable stepsize and variable order implementation of the new LIMM methods shows measurable performance improvement over a similar BDF implementation.
Keywords:
time integration
ODEs
linear multistep methods
linearly implicit schemes
Journal
IF:
2.6
Papers:
5.1K
Citations:
1.8W
Organization
No organization information available