  For many systems of differential equations modeling problems in science and
engineering, there are often natural splittings of the right hand side into two
parts, one of which is non-stiff or mildly stiff, and the other part is stiff.
Such systems can be efficiently treated by a class of implicit-explicit (IMEX)
diagonally implicit multistage integration methods (DIMSIMs), where the stiff
part is integrated by implicit formula, and the non-stiff part is integrated by
an explicit formula. We will construct methods where the explicit part has
strong stability preserving (SSP) property, and the implicit part of the method
is $A$-, or $L$-stable. We will also investigate stability of these methods
when the implicit and explicit parts interact with each other. To be more
precise, we will monitor the size of the region of absolute stability of the
IMEX scheme, assuming that the implicit part of the method is $A$-, or
$L$-stable. Finally we furnish examples of SSP IMEX DIMSIMs up to the order
four with good stability properties.

Numerical Analysis