# The ARKode Solver¶

The ARKode solver library provides an adaptive-step time integration package for stiff, nonstiff and mixed systems of ordinary differential equations (ODEs) given in linearly-implicit form,

$M \dot{y} = f_E(t,y) + f_I(t,y).$

Here,

• $$t$$ is the independent variable (e.g. time),
• $$y$$ is the set of dependent variables (in $$\mathbb R^N$$),
• $$M$$ is a user-specified, non-singular linear operator from $$\mathbb R^N \to \mathbb R^N$$ (the “mass matrix”, possibly time dependent, but independent of $$y$$),
• $$f_E(t,y)$$ is the portion of the right-hand side containing the nonstiff time scale components in the system that should be integrated explicitly, and
• $$f_I(t,y)$$ is the portion of the right-hand side containing the stiff time scale components to be integrated implicitly.

Either of the operators $$f_E$$ or $$f_I$$ may be disabled, allowing for fully explicit, fully implicit, or combination implicit-explicit (IMEX) time integration.

ARKode is a component of the SUNDIALS suite of nonlinear and differential/algebraic equation solvers.

ARKode is written in C, with C++ and Fortran interfaces.

## News¶

Date Details
26 Sep 2016 Major feature addition/bugfix release, included with SUNDIALS v2.7.0
3 Aug 2015 Minor feature addition/bugfix release, included with SUNDIALS v2.6.2
30 Mar 2015 Minor bugfix release, included with SUNDIALS v2.6.1
13 Mar 2015 First official ARKode release, included in the SUNDIALS v2.6.0 release
25 Feb 2014 Beta version of ARKode released, the public source code repository is open (see the Downloads page).

## Contents¶

The remainder of this site is organized into the following topics:

## Support¶

This work is supported by the U.S. Department of Energy through the FASTMath SciDAC Institute, under subcontract B598130 from Lawrence Livermore National Laboratory.