After doing some research, I've found that most of the literature on operator splitting methods (e.g. Strang Splitting, Fractional Step, etc.) are specifically designed for a standard problem type of the form:$$u'=(A+B)u.$$In my application, I have a slightly different form:$$Mu'=(A+B)u$$where $M$ is not the identity operator.  Can the same methodologies be applied when an operator is applied to the $u'$ term?  Are there any other numerical methods to handle this case specific case there $M$ is not the identity operator?  In particular, I'm looking at a case where $M$ is singular.UpdateTo put my particular problem into greater context, my operator is $$M=\left[\begin{array}{cc} 0 & 0 \\ I & I\end{array}\right]$$and $$u=\left[\begin{array}{c} u_1 \\ u_2 \end{array}\right]$$
Operator Splitting methods for DAEs
operator splitting