New insights in solving distributed system equations by the quadrature method-II. Numerical experiments

The results of a series of numerical experiments are presented to verify some of the important points made in Part I of this paper. First, the numerical solutions of various linear and nonlinear differential equations, which were obtained by following the proposed general procedure, are compared with the analytical solutions. It can be observed that a high degree of accuracy is achieved in every case. Second, quadrature coefficients determined by using the explicit formulae derived in this work are shown to be more superior than those by the conventional approach of inverting the Vandermonde matrix. Third, the suggested grid point placement scheme is demonstrated to be better than any other available choice, including the one adopted in the orthogonal collocation method. Finally, the developed techniques are applied to obtain the solution of a chemical engineering problem.