Solving implicit differential equations on parallel computers

We construct and analyse three methods for solving initial value problems for implicit differential equations (IDEs) on parallel computer systems. The first IDE method can be applied to general IDEs of higher index, the other two methods can be applied to partitioned (or semi-explicit) IDEs. The partitioned IDE methods both exploit the special form of the problem and often converge faster than the general IDE method. The first partitioned IDE method is suitable for higher-index problems, the second partitioned IDE method only applies to index 1 problems, but possesses more parallelism across the method. The convergence of these methods is illustrated by solving implicit IDEs of index 0 until 3 that are taken from the literature.