2.7. ARKODE Constants

Below we list all input and output constants used by the main solver, timestepper, and linear solver modules, together with a short description of their meaning. Table 2.15 contains the ARKODE input constants, and Table 2.16 contains the ARKODE output constants.

Table 2.15 ARKODE input constants

Shared input constants
ARK_NORMAL	Solver should return at a specified output time.
ARK_ONE_STEP	Solver should return after each successful step.
Full right-hand side evaluation constants
ARK_FULLRHS_START	Calling the full right-hand side function at the start of the integration.
ARK_FULLRHS_END	Calling the full right-hand side function at the end of a step.
ARK_FULLRHS_OTHER	Calling the full right-hand side function at the some other point e.g., for dense output.
Interpolation module input constants
ARK_INTERP_NONE	Disables polynomial interpolation for dense output.
ARK_INTERP_HERMITE	Specifies use of the Hermite polynomial interpolation module (for non-stiff problems).
ARK_INTERP_LAGRANGE	Specifies use of the Lagrange polynomial interpolation module (for stiff problems).
ARK_INTERP_MAX_DEGREE	Maximum possible interpolating polynomial degree.
Relaxation module input constants
ARK_RELAX_BRENT	Specifies Brent’s method as the relaxation nonlinear solver.
ARK_RELAX_NEWTON	Specifies Newton’s method as the relaxation nonlinear solver.
Default explicit Butcher tables
ARKSTEP_DEFAULT_ERK_1	Use ARKStep’s default first-order ERK method ARKODE_FORWARD_EULER_1_1.
ARKSTEP_DEFAULT_ERK_2	Use ARKStep’s default second-order ERK method ARKODE_RALSTON_3_1_2.
ARKSTEP_DEFAULT_ERK_3	Use ARKStep’s default third-order ERK method ARKODE_BOGACKI_SHAMPINE_4_2_3.
ARKSTEP_DEFAULT_ERK_4	Use ARKStep’s default fourth-order ERK method ARKODE_SOFRONIOU_SPALETTA_5_3_4.
ARKSTEP_DEFAULT_ERK_5	Use ARKStep’s default fifth-order ERK method ARKODE_TSITOURAS_7_4_5.
ARKSTEP_DEFAULT_ERK_6	Use ARKStep’s default sixth-order ERK method ARKODE_VERNER_9_5_6.
ARKSTEP_DEFAULT_ERK_7	Use ARKStep’s default seventh-order ERK method ARKODE_VERNER_10_6_7.
ARKSTEP_DEFAULT_ERK_8	Use ARKStep’s default eighth-order ERK method ARKODE_VERNER_13_7_8.
ARKSTEP_DEFAULT_ERK_9	Use ARKStep’s default ninth-order ERK method ARKODE_VERNER_16_8_9.
ERKSTEP_DEFAULT_1	Use ERKStep’s default first-order ERK method ARKODE_FORWARD_EULER_1_1.
ERKSTEP_DEFAULT_2	Use ERKStep’s default second-order ERK method ARKODE_RALSTON_3_1_2.
ERKSTEP_DEFAULT_3	Use ERKStep’s default third-order ERK method ARKODE_BOGACKI_SHAMPINE_4_2_3.
ERKSTEP_DEFAULT_4	Use ERKStep’s default fourth-order ERK method ARKODE_SOFRONIOU_SPALETTA_5_3_4.
ERKSTEP_DEFAULT_5	Use ERKStep’s default fifth-order ERK method ARKODE_TSITOURAS_7_4_5.
ERKSTEP_DEFAULT_6	Use ERKStep’s default sixth-order ERK method ARKODE_VERNER_9_5_6.
ERKSTEP_DEFAULT_7	Use ERKStep’s default seventh-order ERK method ARKODE_VERNER_10_6_7.
ERKSTEP_DEFAULT_8	Use ERKStep’s default eighth-order ERK method ARKODE_VERNER_13_7_8.
ERKSTEP_DEFAULT_9	Use ERKStep’s default ninth-order ERK method ARKODE_VERNER_16_8_9.
Default implicit Butcher tables
ARKSTEP_DEFAULT_DIRK_1	Use ARKStep’s default first-order DIRK method ARKODE_BACKWARD_EULER_1_1.
ARKSTEP_DEFAULT_DIRK_2	Use ARKStep’s default second-order DIRK method ARKODE_ARK2_DIRK_3_1_2.
ARKSTEP_DEFAULT_DIRK_3	Use ARKStep’s default third-order DIRK method ARKODE_ESDIRK325L2SA_5_2_3.
ARKSTEP_DEFAULT_DIRK_4	Use ARKStep’s default fourth-order DIRK method ARKODE_ESDIRK436L2SA_6_3_4.
ARKSTEP_DEFAULT_DIRK_5	Use ARKStep’s default fifth-order DIRK method ARKODE_ESDIRK547L2SA2_7_4_5.
Default ImEx Butcher tables
ARKSTEP_DEFAULT_ARK_ETABLE_2 & ARKSTEP_DEFAULT_ARK_ITABLE_2	Use ARKStep’s default second-order ARK method (ARKODE_ARK2_ERK_3_1_2 and ARKODE_ARK2_DIRK_3_1_2).
ARKSTEP_DEFAULT_ARK_ETABLE_3 & ARKSTEP_DEFAULT_ARK_ITABLE_3	Use ARKStep’s default third-order ARK method (ARKODE_ARK324L2SA_ERK_4_2_3 and ARKODE_ARK324L2SA_DIRK_4_2_3).
ARKSTEP_DEFAULT_ARK_ETABLE_4 & ARKSTEP_DEFAULT_ARK_ITABLE_4	Use ARKStep’s default fourth-order ARK method (ARKODE_ARK436L2SA_ERK_6_3_4 and ARKODE_ARK436L2SA_DIRK_6_3_4).
ARKSTEP_DEFAULT_ARK_ETABLE_5 & ARKSTEP_DEFAULT_ARK_ITABLE_5	Use ARKStep’s default fifth-order ARK method (ARKODE_ARK548L2SA_ERK_8_4_5 and ARKODE_ARK548L2SA_DIRK_8_4_5).
LSRK method types
ARKODE_LSRK_RKC_2	2nd order Runge-Kutta-Chebyshev (RKC) method ARKODE_LSRK_RKC_2
ARKODE_LSRK_RKL_2	2nd order Runge-Kutta-Legendre (RKL) method ARKODE_LSRK_RKL_2
ARKODE_LSRK_SSP_S_2	Optimal 2nd order s-stage SSP RK method ARKODE_LSRK_SSP_S_2
ARKODE_LSRK_SSP_S_3	Optimal 3rd order s-stage SSP RK method ARKODE_LSRK_SSP_S_3
ARKODE_LSRK_SSP_10_4	Optimal 4th order 10-stage SSP RK method ARKODE_LSRK_SSP_10_4
MRI method types
MRISTEP_EXPLICIT	Use an explicit (at the slow time scale) MRI method.
MRISTEP_IMPLICIT	Use an implicit (at the slow time scale) MRI method.
MRISTEP_IMEX	Use an ImEx (at the slow time scale) MRI method.
Default MRI coupling tables
MRISTEP_DEFAULT_EXPL_1	Use MRIStep’s default 1st-order explicit method (ARKODE_MRI_GARK_FORWARD_EULER).
MRISTEP_DEFAULT_EXPL_2	Use MRIStep’s default 2nd-order explicit method (ARKODE_MRI_GARK_ERK22b).
MRISTEP_DEFAULT_EXPL_3	Use MRIStep’s default 3rd-order explicit method (ARKODE_MIS_KW3).
MRISTEP_DEFAULT_EXPL_4	Use MRIStep’s default 4th-order explicit method (ARKODE_MRI_GARK_ERK45a).
MRISTEP_DEFAULT_EXPL_2_AD	Use MRIStep’s default 2nd-order adaptive explicit method (ARKODE_MRI_GARK_ERK22a).
MRISTEP_DEFAULT_EXPL_3_AD	Use MRIStep’s default 3rd-order adaptive explicit method (ARKODE_MRI_GARK_ERK33a).
MRISTEP_DEFAULT_EXPL_4_AD	Use MRIStep’s default 4th-order adaptive explicit method (ARKODE_MRI_GARK_ERK45a).
MRISTEP_DEFAULT_EXPL_5_AD	Use MRIStep’s default 5th-order adaptive explicit method (ARKODE_MERK54).
MRISTEP_DEFAULT_IMPL_SD_1	Use MRIStep’s default 1st-order solve-decoupled implicit method (ARKODE_MRI_GARK_BACKWARD_EULER).
MRISTEP_DEFAULT_IMPL_SD_2	Use MRIStep’s default 2nd-order solve-decoupled implicit method (ARKODE_MRI_GARK_IRK21a).
MRISTEP_DEFAULT_IMPL_SD_3	Use MRIStep’s default 3rd-order solve-decoupled implicit method (ARKODE_MRI_GARK_ESDIRK34a).
MRISTEP_DEFAULT_IMPL_SD_4	Use MRIStep’s default 4th-order solve-decoupled implicit method (ARKODE_MRI_GARK_ESDIRK46a).
MRISTEP_DEFAULT_IMEX_SD_1	Use MRIStep’s default 1st-order solve-decoupled ImEx method (ARKODE_IMEX_MRI_GARK_EULER).
MRISTEP_DEFAULT_IMEX_SD_2	Use MRIStep’s default 2nd-order solve-decoupled ImEx method (ARKODE_IMEX_MRI_GARK_TRAPEZOIDAL).
MRISTEP_DEFAULT_IMEX_SD_3	Use MRIStep’s default 3rd-order solve-decoupled ImEx method (ARKODE_IMEX_MRI_GARK3b).
MRISTEP_DEFAULT_IMEX_SD_4	Use MRIStep’s default 4th-order solve-decoupled ImEx method (ARKODE_IMEX_MRI_GARK4).
MRISTEP_DEFAULT_IMEX_SD_2_AD	Use MRIStep’s default 2nd-order solve-decoupled adaptive ImEx method (ARKODE_IMEX_MRI_SR21).
MRISTEP_DEFAULT_IMEX_SD_3_AD	Use MRIStep’s default 3rd-order solve-decoupled adaptive ImEx method (ARKODE_IMEX_MRI_SR32).
MRISTEP_DEFAULT_IMEX_SD_4_AD	Use MRIStep’s default 4th-order solve-decoupled adaptive ImEx method (ARKODE_IMEX_MRI_SR43).

Table 2.16 ARKODE output constants

Shared output constants
ARK_SUCCESS	0	Successful function return.
ARK_TSTOP_RETURN	1	ARKODE succeeded by reaching the specified stopping point.
ARK_ROOT_RETURN	2	ARKODE succeeded and found one more more roots.
ARK_WARNING	99	ARKODE succeeded but an unusual situation occurred.
ARK_TOO_MUCH_WORK	-1	The solver took mxstep internal steps but could not reach tout.
ARK_TOO_MUCH_ACC	-2	The solver could not satisfy the accuracy demanded by the user for some internal step.
ARK_ERR_FAILURE	-3	Error test failures occurred too many times during one internal time step, or the minimum step size was reached.
ARK_CONV_FAILURE	-4	Convergence test failures occurred too many times during one internal time step, or the minimum step size was reached.
ARK_LINIT_FAIL	-5	The linear solver’s initialization function failed.
ARK_LSETUP_FAIL	-6	The linear solver’s setup function failed in an unrecoverable manner.
ARK_LSOLVE_FAIL	-7	The linear solver’s solve function failed in an unrecoverable manner.
ARK_RHSFUNC_FAIL	-8	The right-hand side function failed in an unrecoverable manner.
ARK_FIRST_RHSFUNC_ERR	-9	The right-hand side function failed at the first call.
ARK_REPTD_RHSFUNC_ERR	-10	The right-hand side function had repeated recoverable errors.
ARK_UNREC_RHSFUNC_ERR	-11	The right-hand side function had a recoverable error, but no recovery is possible.
ARK_RTFUNC_FAIL	-12	The rootfinding function failed in an unrecoverable manner.
ARK_LFREE_FAIL	-13	The linear solver’s memory deallocation function failed.
ARK_MASSINIT_FAIL	-14	The mass matrix linear solver’s initialization function failed.
ARK_MASSSETUP_FAIL	-15	The mass matrix linear solver’s setup function failed in an unrecoverable manner.
ARK_MASSSOLVE_FAIL	-16	The mass matrix linear solver’s solve function failed in an unrecoverable manner.
ARK_MASSFREE_FAIL	-17	The mass matrix linear solver’s memory deallocation function failed.
ARK_MASSMULT_FAIL	-18	The mass matrix-vector product function failed.
ARK_CONSTR_FAIL	-19	The inequality constraint test failed repeatedly or failed with the minimum step size.
ARK_MEM_FAIL	-20	A memory allocation failed.
ARK_MEM_NULL	-21	The arkode_mem argument was NULL.
ARK_ILL_INPUT	-22	One of the function inputs is illegal.
ARK_NO_MALLOC	-23	The ARKODE memory block was not allocated by a call to ARKStepCreate(), ERKStepCreate(), or MRIStepCreate().
ARK_BAD_K	-24	The derivative order \(k\) is larger than allowed.
ARK_BAD_T	-25	The time \(t\) is outside the last step taken.
ARK_BAD_DKY	-26	The output derivative vector is NULL.
ARK_TOO_CLOSE	-27	The output and initial times are too close to each other.
ARK_VECTOROP_ERR	-28	An error occurred when calling an N_Vector routine.
ARK_NLS_INIT_FAIL	-29	An error occurred when initializing a SUNNonlinSol module.
ARK_NLS_SETUP_FAIL	-30	A non-recoverable error occurred when setting up a SUNNonlinSol module.
ARK_NLS_SETUP_RECVR	-31	A recoverable error occurred when setting up a SUNNonlinSol module.
ARK_NLS_OP_ERR	-32	An error occurred when calling a set/get routine in a SUNNonlinSol module.
ARK_INNERSTEP_ATTACH_ERR	-33	An error occurred when attaching the inner stepper module.
ARK_INNERSTEP_FAIL	-34	An error occurred in the inner stepper module.
ARK_PREINNERFN_FAIL	-35	An error occurred in the MRIStep pre inner integrator function.
ARK_POSTINNERFN_FAIL	-36	An error occurred in the MRIStep post inner integrator function.
ARK_INTERP_FAIL	-40	An error occurred in the ARKODE polynomial interpolation module.
ARK_INVALID_TABLE	-41	An invalid Butcher or MRI table was encountered.
ARK_CONTEXT_ERR	-42	An error occurred with the SUNDIALS context object
ARK_RELAX_FAIL	-43	An error occurred in computing the relaxation parameter
ARK_RELAX_MEM_FAIL	-44	The relaxation memory structure is NULL
ARK_RELAX_FUNC_FAIL	-45	The relaxation function returned an unrecoverable error
ARK_RELAX_JAC_FAIL	-46	The relaxation Jacobian function returned an unrecoverable error
ARK_CONTROLLER_ERR	-47	An error with a SUNAdaptController object was encountered.
ARK_STEPPER_UNSUPPORTED	-48	An operation was not supported by the current time-stepping module.
ARK_DOMEIG_FAIL	-49	The dominant eigenvalue function failed. It is either not provided or returns an illegal value.
ARK_MAX_STAGE_LIMIT_FAIL	-50	Stepper failed to achieve stable results. Either reduce the step size or increase the stage_max_limit
ARK_SUNSTEPPER_ERR	-51	An error occurred in the SUNStepper module.
ARK_STEP_DIRECTION_ERR	-52	An error occurred changing the step direction.
ARK_ADJ_CHECKPOINT_FAIL	-53	An occurred when checkpointing a state during the adjoint integration.
ARK_ADJ_RECOMPUTE_FAIL	-54	An occurred recomputing steps during the adjoint integration.
ARK_SUNADJSTEPPER_ERR	-55	An error occurred in the SUNAdjStepper module.
ARK_DEE_FAIL	-56	An error occurred in the SUNDomEigEstimator module.
ARK_UNRECOGNIZED_ERROR	-99	An unknown error was encountered.
ARKLS linear solver module output constants
ARKLS_SUCCESS	0	Successful function return.
ARKLS_MEM_NULL	-1	The arkode_mem argument was NULL.
ARKLS_LMEM_NULL	-2	The ARKLS linear solver interface has not been initialized.
ARKLS_ILL_INPUT	-3	The ARKLS solver interface is not compatible with the current N_Vector module, or an input value was illegal.
ARKLS_MEM_FAIL	-4	A memory allocation request failed.
ARKLS_PMEM_NULL	-5	The preconditioner module has not been initialized.
ARKLS_MASSMEM_NULL	-6	The ARKLS mass-matrix linear solver interface has not been initialized.
ARKLS_JACFUNC_UNRECVR	-7	The Jacobian function failed in an unrecoverable manner.
ARKLS_JACFUNC_RECVR	-8	The Jacobian function had a recoverable error.
ARKLS_MASSFUNC_UNRECVR	-9	The mass matrix function failed in an unrecoverable manner.
ARKLS_MASSFUNC_RECVR	-10	The mass matrix function had a recoverable error.
ARKLS_SUNMAT_FAIL	-11	An error occurred with the current SUNMatrix module.
ARKLS_SUNLS_FAIL	-12	An error occurred with the current SUNLinearSolver module.

enum ARKRelaxSolver

Nonlinear solver identifiers used to specify the method for solving (2.67) when relaxation is enabled.

enumerator ARK_RELAX_NEWTON

Newton’s method

enumerator ARK_RELAX_BRENT

Brent’s method