1: typedef struct _RKTableau *RKTableau;
  2: struct _RKTableau {
  3:   char       *name;
  4:   PetscInt   order;               /* Classical approximation order of the method i              */
  5:   PetscInt   s;                   /* Number of stages                                           */
  6:   PetscInt   p;                   /* Interpolation order                                        */
  7:   PetscBool  FSAL;                /* flag to indicate if tableau is FSAL                        */
  8:   PetscReal  *A,*b,*c;            /* Tableau                                                    */
  9:   PetscReal  *bembed;             /* Embedded formula of order one less (order-1)               */
 10:   PetscReal  *binterp;            /* Dense output formula                                       */
 11:   PetscReal  ccfl;                /* Placeholder for CFL coefficient relative to forward Euler  */
 12: };
 13: typedef struct _RKTableauLink *RKTableauLink;
 14: struct _RKTableauLink {
 15:   struct _RKTableau tab;
 16:   RKTableauLink     next;
 17: };

 19: typedef struct {
 20:   RKTableau    tableau;
 21:   Vec          X0;
 22:   Vec          *Y;               /* States computed during the step                                              */
 23:   Vec          *YdotRHS;         /* Function evaluations for the non-stiff part and contains all components      */
 24:   Vec          *YdotRHS_fast;    /* Function evaluations for the non-stiff part and contains fast components     */
 25:   Vec          *YdotRHS_slow;    /* Function evaluations for the non-stiff part and contains slow components     */
 26:   Vec          *VecsDeltaLam;    /* Increment of the adjoint sensitivity w.r.t IC at stage                       */
 27:   Vec          *VecsSensiTemp;
 28:   Vec          VecDeltaMu;       /* Increment of the adjoint sensitivity w.r.t P at stage                        */
 29:   Vec          *VecsDeltaLam2;   /* Increment of the 2nd-order adjoint sensitivity w.r.t IC at stage */
 30:   Vec          VecDeltaMu2;      /* Increment of the 2nd-order adjoint sensitivity w.r.t P at stage */
 31:   Vec          *VecsSensi2Temp;
 32:   PetscScalar  *work;            /* Scalar work                                                                  */
 33:   PetscInt     slow;             /* flag indicates call slow components solver (0) or fast components solver (1) */
 34:   PetscReal    stage_time;
 35:   TSStepStatus status;
 36:   PetscReal    ptime;
 37:   PetscReal    time_step;
 38:   PetscInt     dtratio;          /* ratio between slow time step size and fast step size                         */
 39:   IS           is_fast,is_slow;
 40:   TS           subts_fast,subts_slow,subts_current,ts_root;
 41:   PetscBool    use_multirate;
 42:   Mat          MatFwdSensip0;
 43:   Mat          *MatsFwdStageSensip;
 44:   Mat          *MatsFwdSensipTemp;
 45:   Vec          VecDeltaFwdSensipCol; /* Working vector for holding one column of the sensitivity matrix */
 46: } TS_RK;