Evaluation of Weighted Residual Methods for the Solution of the Chemical Reactor Pellet Model Equations

Techniques in the family of weighted residual methods; the orthogonal collocation, Galerkin, tau, and least-squares methods, are adopted to solve a non-linear and highly coupled pellet problem. Based on a residual measure and problem matrix condition numbers, the Galerkin and tau methods are favorable solution techniques for the pellet equations. On the other hand, the orthogonal collocation is associated with less theoretical complexities and the simplest implementation. The accuracy of the orthogonal collocation method is similar to the least-squares method but with smaller condition numbers.