A parallel nearly implicit time-stepping scheme

Across-the-space parallelism still remains the most mature, convenient and natural way to parallelize large scale problems. One of the major problems here is that implicit time stepping is often difficult to parallelize due to the structure of the system. Approximate implicit schemes have been suggested to circumvent the problem (M.A. Botchev et al., Appl. Numer. Math. 31 (3) (1999) 239). These schemes have attractive stability properties and they are also very well parallelizable.The purpose of this article is to give an overall assessment of the parallelism of the method.