Runge-Kutta-Gill numerical integration

These two first-order ODEs for I a and Q must be solved simultaneously, with assistance from equation (19-28) for components B, C, and D. The fourth-order Runge-Kutta-Gill numerical integration scheme can be implemented if both... 

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. 

The steady-state heat and mass balance equations of the different models were numerically integrated using a fourth-order Runge-Kutta-Gill method for the one-dimensional models, while the Crank-Nicholson finite differences method was used to solve the two-dimensional models. 

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 ... 

---