Efficient parallel predictor-corrector methods (Q1902088)

A class of parallel predictor-corrector methods for non-stiff problems introduced by the author and other co-workers in a previous paper is re-examined. The methods are a class of general linear methods, including Adams-Bashforth-Radau methods in particular. A modification to the methods is derived which increases the stage order and leads to improved convergence characteristics and stability. The improved methods can be implemented in a parallel environment at no extra cost. The numerical tests show a speedup of about 3.1 over a good sequential Runge-Kutta code.