  We construct splitting methods for the solution of the equations of
magnetohydrodynamics (MHD). Due to the physical significance of the involved
operators, splittings into three or even four operators with positive
coefficients are appropriate for a physically correct and efficient solution of
the equations. To efficiently obtain an accurate solution approximation,
adaptive choice of the time-steps is important particularly in the light of the
unsmooth dynamics of the system. Thus, we construct new method coefficients in
conjunction with associated error estimators by optimizing the leading local
error term. As a proof of concept, we demonstrate that adaptive splitting
faithfully reflects the solution behavior also in the presence of a shock for
the viscous Burgers equation, which serves as a simplified model problem
displaying several features of the Navier-Stokes equation for incompressible
flow.
