  In numerical time-integration with implicit-explicit (IMEX) methods, a
within-step adaptable decomposition called residual balanced decomposition is
introduced. With this decomposition, the requirement of a small enough residual
in the iterative solver can be removed, consequently, this allows to exchange
stability for efficiency. This decomposition transfers any residual occurring
in the implicit equation of the implicit-step into the explicit part of the
decomposition. By balancing the residual, the accuracy of the local truncation
error of the time-stepping method becomes independent from the accuracy by
which the implicit equation is solved. In order to balance the residual, the
original IMEX decomposition is adjusted after the iterative solver has been
stopped. For this to work, the traditional IMEX time-stepping algorithm needs
to be changed. We call this new method the shortcut-IMEX (SIMEX). SIMEX can
gain computational efficiency by exploring the trade-off between the
computational effort placed in solving the implicit equation and the size of
the numerically stable time-step. Typically, increasing the number of solver
iterations increases the largest stable step-size. Both multi-step and
Runge-Kutta (RK) methods are suitable for use with SIMEX. Here, we show the
efficiency of a SIMEX-RK method in overcoming parabolic stiffness by applying
it to a nonlinear reaction-advection-diffusion equation. In order to define a
stability region for SIMEX, a region in the complex plane is depicted by
applying SIMEX to a suitable PDE model containing diffusion and dispersion. A
myriad of stability regions can be reached by changing the RK tableau and the
solver.
