Runge-Kutta-Merson method

The integration, between YA = Y. and YA = Y, can be carried out by the Runge-Kutta-Merson method. For gooa accuracy, the intervals have to be very small. For this calculation, the correct values of ky-k% must be known. If periodic deviations are obtained between the experimental (from the FCCU) yields and the yields predicted by this model, a corrective factor in these k values can be introduced. 

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. 

EROS handles concurrent reactions with a kinetic modeling approach, where the fastest reaction has the highest probability to occur in a mixture. The data for the kinetic model are derived from relative or sometimes absolute reaction rate constants. Rates of different reaction paths are obtained by evaluation mechanisms included in the rule base that lead to partial differential equations for the reaction rate. Three methods are available that cover the integration of the differential equations the GEAR algorithm, the Runge-Kutta method, and the Runge-Kutta-Merson method [120,121], The estimation of a reaction rate is not always possible. In this case, probabilities for the different reaction pathways are calculated based on probabilities for individual reaction steps. 

BzzOdeRKM. Fourth-order Runge-Kutta-Merson method. 

The mathematical model implemented is based on differential equations of heat and mass transfer along the time and they are numerically solved using the Runge-Kutta-Merson method. The final program is implemented in Fortran. Different time steps delta t = 0.001 s and 0.0001s) were used for the numerical integration and the same results were obtained. The objective of the software is to estimate temperatures and humidity in the different parts of the body, as function of time (Teixeira et al., 2010). 

Runge-Kutta Merson method of numerical integration was used for the solution of this equation. 

Runge-Kutta-Merson outlines a process for deciding the step size for a better predetermined accuracy. For this method, five functions are evaluated at every step. The algorithm is... 

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