Introduction

The following tables summarize the salient features of each of the example problems in this document. Each example is designed to be relatively self-contained, so that you need only study and/or emulate the problem that is most closely related to your own. We group these examples according to programming language (C, C++, Fortran).

ARKODE example problems written in C are summarized in the table below, and are further described in the chapters Serial C example problems, OpenMP C example problems, Parallel C example problems and Parallel Hypre example problems.

Problem	Integrator	Nonlinear	Linear	Size	Extras
ark_analytic	DIRK	Newton	Dense	1
ark_analytic_nonlin	ERK	N.A.	N.A.	1	ERKStep timestepping module
ark_brusselator	DIRK	Newton	Dense	3
ark_brusselator_fp	ARK	Fixed-point	N.A.	3
ark_robertson	DIRK	Newton	Dense	3
ark_robertson_root	DIRK	Newton	Dense	3	rootfinding
ark_brusselator1D	DIRK	Newton	Band	3N
ark_brusselator1D_omp	DIRK	Newton	Band	3N	OpenMP-enabled
ark_brusselator1D_klu	DIRK	Newton	KLU	3N	sparse matrices
ark_brusselator1D_FEM_slu	DIRK	Newton	SuperLU_MT	3N	finite-element, \(M\ne I\), sparse matrices
ark_heat1D	DIRK	Newton	PCG	N
ark_heat1D_adapt	DIRK	Newton	PCG	(dynamic)	adaptive vector resizing
ark_KrylovDemo_prec	DIRK	Newton	SPGMR	216	multiple preconditioners
ark_diurnal_kry_bbd_p	DIRK	Newton	SPGMR	200	parallel, BBD preconditioner
ark_diurnal_kry_p	DIRK	Newton	SPGMR	200	parallel, block-diagonal precond.
ark_diurnal_kry_ph	DIRK	Newton	SPGMR	200	HYPRE parallel vector

ARKODE example problems written in C++ are summarized in the table below, and are further described in the chapters Serial C++ example problems and Parallel C++ example problems.

Problem	Integrator	Nonlinear	Linear	Size	Extras
ark_analytic_sys	DIRK	Newton	Dense	3
ark_heat2D	DIRK	Newton	PCG	\(nx*ny\)	parallel