Let c_eff be the minimum number of function evaluations required to step as far as one step of forward Euler while Many brstill being SSP. Some theoretical bounds Many br
1. There are no explicit methods with c_eff > 1. Many br
2. There are no explicit methods beyond order 4 (for nonlinear problems) and c_eff > 0. Many br
3. There are no implicit methods with order greater than 1 and c_eff > 2. Many br
This integrator provides Runge-Kutta methods of order 2, 3, and 4 with maximal values of c_eff. More stages allows Many brfor larger values of c_eff which improves efficiency. These implementations are low-memory and only use 2 or 3 work Many brvectors regardless of the total number of stages, so e.g. 25-stage 3rd order methods may be an excellent choice. Many br
Methods can be chosen with -ts_ssp_type {rks2,rks3,rk104} Many br
rks2: Second order methods with any number s>1 of stages. c_eff = (s-1)/s Many br
rks3: Third order methods with s=n^2 stages, n>1. c_eff = (s-n)/s Many br
rk104: A 10-stage fourth order method. c_eff = 0.6 Many br
Many br
1. | - Ketcheson, Highly efficient strong stability preserving Runge Kutta methods with low storage implementations, SISC, 2008. Many br | |
2. | - Gottlieb, Ketcheson, and Shu, High order strong stability preserving time discretizations, J Scientific Computing, 2009. Many br |
Level:beginner
Location:src/ts/impls/explicit/ssp/ssp.c
Index of all TS routines
Table of Contents for all manual pages
Index of all manual pages