In recent years, new and more effective procedures for applying collocation have been published. This article is devoted to present a revision of this subject and complement its developments. From the general theory two broad approaches are derived, which yield the direct and the indirect TH-collocation methods. The former approach had not been published before, and it is a dual of the indirect...

rigorous mathematical modeling of adsorption processes in packed beds involves time-consuming computations which are considered as the fundamental weakness of such thorough mathematical models. thus, reducing the computation time was a key factor in improving adsorption mathematical models. in order to achieve this goal, an attempt was made to know how much using different numerical methods inf...

The Chebyshev orthogonal collocation is a powerful and accurate numerical technique, which is also relatively easy to implement using modern mathematical software (e.g., MATHEMATICA and MATLAB). This technique allows the elucidation of engineering problems involving partial differentials equations or boundary value problems. Six chemical engineering problems concerning the transfer of momentum,...

Abstract. A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian satisfies a strong convexity condition, then the discrete problem possesses a local minimizer in a neighborhood of the continuous solution, and as the...

Fast direct methods are presented for the solution of linear systems arising in highorder, tensor-product orthogonal spline collocation applied to separable, second order, linear, elliptic partial di erential equations on rectangles. The methods, which are based on a matrix decomposition approach, involve the solution of a generalized eigenvalue problem corresponding to the orthogonal spline co...

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...

The paper proposed to use a Recurrent Neural Network Model (RNNM) and a dynamic Backpropagation learning for centralized identification of an anaerobic digestion bioprocess, carried out in a fixed bed and a recirculation tank of a wastewater treatment system. The anaerobic digestion bioprocess represented a distributed parameter system, described by partial differential equations. The analytica...

In this work, we analyse new robust spline approximation methods for mth order boundary value problems described by nonlinear ordinary diierential and integro-diierential equations with m linear boundary conditions. Our main aim is to introduce a cost-eeective alternative to the highly successful orthogonal col-location method, and to prove stability and convergence properties similar to the or...