Efficient parallel predictor-corrector methods Original Research Article

Recently, the so-called Adams-Bashforth-Radau (ABR) methods were proposed by van der Houwen et al. (1994). An ABR method is a high-order parallel predictor-corrector method for solving non-stiff initial value problems, based on a combination of Adams-Bashforth and Radau formulas. Comparison of ABR with the famous sequential 8(7) Runge-Kutta method of Dormand and Prince showed speed-up factors of about 2.7. In this paper we improve the ABR methods by making them more accurate without any additional costs. This improved version increases the speed-up factor on the average to 3.1.