Constraint preserving integrators for general nonlinear higher index DAEs
In the last few years there has been considerable research on numerical methods for differential algebraic equations (DAEs), \(f(x', x, t)= 0\), where \(f_{x'}\) is identically singular. The index provides one measure of the singularity of a DAE. Most of the numerical analysis literature on DAEs to date has dealt with DAEs with indices no larger than three. Even in this case, the systems were often assumed to have a special structure. Recently a numerical method was proposed that could, in principle, be used to integrate general unstructured higher index solvable DAEs. However, that method did not preserve constraints. This paper discusses a modification of that approach which can be used to design constraint preserving integrators for general nonlinear higher index DAEs. The method preserves all constraints including higher order and implicit constraints. First it is shown that the obvious approach of using the original explicit integrator followed by a projection will not work in general. Then an alternative based on implicit coordinate partitioning is developed. This is similar to the coordinate partitioning used in mechanics codes except that here all constraints may be implicit and the partitioning must be computed implicitly. To illustrate the feasibility of this approach, a nonlinear fully implicit DAE is solved numerically.
scientific article; zbMATH DE number 739401