Accuracies of numerical solutions of dispersion model by orthogonal collocation method

The dispersion model for a flow chemical reactor was solved by the orthogonal collocation method using collocation constants calculated from equations that were derived by differentiating the Lagrange's interpolation formula. Accuracies of the numerical solutions were examined based on reactant concentrations at the reactor inlet and outlet. From comparisons with analytical solutions for a first-order reaction, it was found that highly accurate solutions of more than 10 significant digits are obtainable with double precision by simply increasing the number of internal collocation points even under severe conditions of large Peclet number and kinetic constant. This result clearly shows that the orthogonal collocation method is superior to the finite-difference method which requires a search for an appropriate step size according to the magnitude of the Peclet number.