Predictor-corrector integration methods

Thus we find that the choice of quaternion variables introduces barriers to efficient symplectic-reversible discretization, typically forcing us to use some off-the-shelf explicit numerical integrator for general systems such as a Runge-Kutta or predictor-corrector method. 

Our discussion so far has considered the use of SHAKE with the Verlet algorithm Versions have also been derived for other integration schemes, such as the leap-froj algorithm, the predictor-corrector methods and the velocity Verlet algorithm. In the cast of the velocity Verlet algorithm, the method has been named RATTLE [Anderson 1983]... 

When the quadrature of eq 2 cannot be performed analytically the integration should be carried out numerically by robust routines such as the Runge-Kutta, Adams-Moulton predictor-corrector or Bulirsch-Stoer methods with step size and error control [53, 55, 56], These routines can also be found in computer codings at Netlib and in standard books on computer codes [53]. 

R. M. Thomas and T. E. Simos, A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrodinger equation, J. Comput. Appl. Math., 1997, 87, 215-226. 

In 26 the authors have developed a new trigonometrically-fitted predictor-corrector (P-C) scheme based on the Adams-Bashforth-Moulton P-C methods. In particular, the predictor is based on the fifth algebraic order Adams-Bashforth scheme and the corrector on the sixth algebraic order Adams-Moulton scheme. More specifically the new developed scheme integrates exactly any linear combination of the functions ... 

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