TSIRK uses the sparse Kronecker product matrix implementation of MATKAIJ to achieve good arithmetic intensity.
Gauss-Legrendre methods are currently supported. These are A-stable symplectic methods with an arbitrary number of stages. The order of accuracy is 2s when using s stages. The default method uses three stages and thus has an order of six. The number of stages (thus order) can be set with -ts_irk_nstages or TSIRKSetNumStages().