Ordinary differential equations Adams-Moulton methods

The GRM using the generalized Maxwell-Stefan equations has no closed-form solutions. Numerical solutions were calculated using a computer program based on an implementation of the method of orthogonal collocation on finite elements [29,62,63]. The set of discretized ordinary differential equations was solved with the Adams-Moulton method, implemented in the VODE procedure [64]. The relative and absolute errors of the numerical calculations were 1 x 10 and 1 x 10 , respectively. 

To integrate the ordinary differential equations resulting fi om space discretization we tried the modified Euler method (which is equivalent to a second-order Runge-Kutta scheme), the third and fourth order Runge-Kutta as well as the Adams-Moulton and Milne predictor-corrector schemes [7, 8]. The Milne method was eliminated from the start, since it was impossible to obtain stability (i.e., convergence to the desired solution) for the step values that were tried. 

The balance equations for column reactors that operate in a concurrent mode as well as for semibatch reactors are mathematically described by ordinary differential equations. Basically, it is an initial value problem, which can be solved by, for example, Runge-Kutta, Adams-Moulton, or BD methods (Appendix 2). Countercurrent column reactor models result in boundary value problems, and they can be solved, for example, by orthogonal collocation [3]. The backmixed model consists of an algebraic equation system that is solved by the Newton-Raphson method (Appendix 1). 

This equation was solved using the LSODE routine from the ODEPACK library. LSODE uses a 12 order Adams-Moulton method to solves a system of ordinary differential equations. 

Solution of a set of nonlinear ordinary differential equations by the Adams-Moulton predictor-corrector method. 

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