  We are motivated to solve differential algebraic equations with new
multi-stage and multisplitting methods. The multi-stage strategy of the
waveform relaxation (WR) methods are given with outer and inner iterations.
While the outer iterations decouple the initial value problem of differential
algebraic equations (DAEs) in the form of $A \frac{d y(t)}{dt} + B y(t) = f(t)$
to $M_A \frac{d y^{k+1}(t)}{dt} + M_1 y^{k+1}(t) = N_1 y^k(t) + N_A \frac{d
y^{k}(t)} + f(t)$, where $A = M_A - N_A$, $B = M_1 - N_1$. The inner iterations
decouple further $M_1 = M_2 - N_2$ and $M_2 = M_3 - N_3$ with additional
iterative processes, such that we result to invert simpler matrices and
accelerate the solver process. The multisplitting method use additional a
decomposition of the outer iterative process with parallel algorithms, based on
the partition of unity, such that we could improve the solver method. We
discuss the different algorithms and present a first experiment based on a DAE
system.
