# The ARKode Solver¶

ARKode is a solver for stiff and nonstiff systems of ordinary differential equations (ODEs) given in explicit 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 $$\Re^N$$),
• $$M$$ is a user-specified, non-singular operator from $$\Re^N \to \Re^N$$ (the “mass matrix”, possibly time dependent, but independent of $$y$$),
• $$f_E(t,y)$$ is the portion of the right-hand side containing the “slow” 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 “fast” time scale components to be integrated implicitly.

Either of the $$f_E$$ or $$f_I$$ operators 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:¶

23 January 2013:
ARKode is still in development. An official release as part of the SUNDIALS suite is planned for summer 2013, but early access to the development repository will be opened up much sooner. Both events will be posted to this page when they occur.

## 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.