Integration step length

CINT Calculation interval or integration step length in fixed step methods. NOCI Used to specify the communication interval as NOCI CINT. 

RERR Permitted relative error per integration step length. 

Under normal circumstances, the use of a characteristic velocity equation of the type shown above can cause difficulties in computation, owing to the existence of an implicit algebraic loop, which must be solved, at every integration step length. In this the appropriate value of L or G satisfying the value of h generated in the differential mass balance equation, must be found as shown in the information flow diagram of Fig. 3.54. 

CINT The calculation interval. This is the integration step length... 

Much effort has been devoted to producing fast and efficient numerical integration techniques, and there is a very wide variety of methods now available. The efficiency of an integration routine depends on the number of function evaluations, required to achieve a given degree of accuracy. The number of evaluations depends both on the complexity of the computation and on the number of integration step lengths. The number of steps depends on both the na-... 

The most common numerical problem, as shown by some of the simulation examples, is that of equation stiffness. This is manifested by the need to use shorter and shorter integration step lengths, with the result that the solution proceeds more and more slowly and may come to a complete halt. Such behaviour is exhibited by systems having combinations of very fast and very slow processes. Stiff systems can also be thought of as consisting of differential equations, having large differences in the process time constants. Sometimes, the... 

For the simulation of the reactor behaviour the system of ordinary differential equations was integrated by means of a Runge-Kutta-Merson method with variable step length, whereas the nonlinear algebraic equations were solved by a Newton-Raphson iteration. 

Remark 1. A trigonometrically-fitted method is not a classical one because it has coefficients which are dependent on the quantity u = wh, where w is the frequency of the problem and h is the step length of the integration. 

Several parameters are useful in describing rearrangement mechanisms. The first is the integrated path length, 5, approximated as a sum over steps, m ... 

The path integral for a jointed-chain polymer, with a step length c, is given by... 

If the local phase-lag error is bounded by acc and the step size of the integration used for the nth step length is h , the estimated step size for the (n + l)st step, which will give a local error bounded by acc, must be... 

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