Predictor-corrector integration

Fig. 10.7. Schematic representation of predictor-corrector integration, such as the integrator used in the...

When a Heun (predictor-corrector) integration scheme is used, a higher accuracy is obtained but at the cost of many supplementary calculations. This is due to... 

The dynamic structural solution for the thrust loading is obtained using a modified-predictor-corrector-integration technique and normal mode theory. 

Figure 6 Two algorithms to conduct Gibbs-Duhem integrations. The pressure route (upper-left) corresponds to integration of Clapey-ron .s equation and entails iVPr-ensemble simulations of both phases (depicted here by the two boxes). The chemical potential route (upper-right) entails p.VT simulations. In both cases, a trapezoidal predictor-corrector integration. scheme is illustrated here the integration advances from point 0 to point 1...

This MP2 direct dynamics trajectory study was performed with the VENUS96/GAUSSIAN98 package of programs, which includes an efficient predictor-corrector integration algorithm and Hessian updating. A... 

The coupled, first-order Hamiltonian equations of motion for the various systems studied were integrated numerically on either a CDC 7600 or a DEC VAX 11/780 digital computer using a variable step-size, fifth-order Adams-Moulton predictor-corrector integration technique As a test of accuracy, rate constants were computed for... 

In contrast to gas-phase classical trajectory calculations, the forces in this system vary rapidly with distance. As a consequence, no computer time advantage is gained by using a high-order predictor-corrector integrator. A low-order predictor-corrector is most efficient computationally. One impact point on a clean metal system with 240 atoms typically takes 120 timesteps, integrates for 2 X 10 seconds and takes about 30 seconds on a CDC 7600 computer. The computer time is approximately proportional to where N is the number of atoms in the system. 

Higher derivatives can be obtained by successive differentiation of equation (10), using the derivatives y, y, etc., which are routinely calculated in predictor-corrector integration schemes. Thus equations (8)-(10) provide the means to calculate the derivatives etc., in equation (7). Once... 

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]... 

A predictor-corrector algorithm for automatic computer-assisted integration of stiff ordinary differential equations. This procedure carries the name of its originator. ... 

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