Algorithm, Rung-Kutta-Gill

Initial numerical simulations of population density dynamics incorporated experimental data of Figures 2 and 4 and Equations 16, 20, 23, and 27 into a Runge-Kutta-Gill integration algorithm (21). The constant k.. was manipulated to obtain an optimum fit, both with respect to sample time and to degree of polymerization. Further modifications were necessary to improve the numerical fit of the population density distribution surface. 

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Runge-Kutta-Gill method provides an efficient algorithm for solving a system of first-order differential equations and makes use of much less computer memory when compared with other numerical methods. 

Numerical methods are required to integrate these coupled ordinary differential equations and to calculate the time-dependent molar density of each component in the exit stream of the first CSTR. Generic integral expressions are illustrated below. The Runge-Kutta-Gill fourth-order correct algorithm is useful to perform this task. 

Numerical methods such as the Runge-Kutta-Gill fourth-order correct integration algorithm are required to simulate the performance of a nonisothermal tubular reactor. In the following sections, the effects of key design parameters on temperature and conversion profiles illustrate important strategies to prevent thermal runaway. 

The Runge-Kutta-Gill fourth-order correct numerical integration algorithm for coupled ODEs is useful to simulate this double-pipe reactor after temperature-and conversion-dependent kinetic rate laws are introduced for both fluids. The generalized procedure is as follows ... 

Step 2. Solve the set of three coupled ODEs from z = 0 to z = L via the appropriate Runge-Kutta-Gill algorithm. 

It was noted earlier that the choice of integration algorithm will depend partially on the mode of operation of the computer center. We would like now to illustrate the role that this factor might play in a decision between the predictor-corrector and the Runge-Kutta-Gill procedures. 

The most widely used single-step method is the Runge-Kutta modification due to Gill, called the Runge-Kutta-Gill algorithm. This algorithm for a vector set of differential equations is... 

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