Abstract
Abstract An efficient numerical method for solution of boundary value problems with additional condition is presented. The approach is based on the shooting method but the procedure of seeking “the proper shot” allows one to satisfy “additional” boundary conditions. General considerations are illustrated by a real example. The computational example concerns the “dead zone” regime for the non-linear diffusion-reaction equation in heterogeneous catalysis. Accuracy and efficiency of the presented method confirm results obtained for a wide range of changes of process parameters, including the vicinity of a critical point. Calculations were performed with the use of the Maple® program.
Highlights
Finite difference methods, volume methods and orthogonal collocation methods are numerical approaches usually employed for solution of chemical engineering boundary-value problems
The most recognizable problem of this type in chemical engineering is the Stefan problem in which a phase boundary can move with time
One can find it in fluid mechanics, combustion, filtration and other fields of chemical engineering
Summary
Finite difference methods, volume methods and orthogonal collocation methods are numerical approaches usually employed for solution of chemical engineering boundary-value problems. If the sufficient conditions are not available, I recommend to use a combination of the algorithms A and C to determine a regime of catalyst pellet work (dead zone exists or not).
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