orthogonal collocation

A hybrid computational procedure of Newton Raphson method and orthogonal collocation method have been applied to study the behavior of nonlinear astrophysics equations. The nonlinear Lane Emden equation has been discretized using the orthogonal collocation method using $n^{th}$-order Bessel polynomial as $J_n(\xi)$ as base function.  The system of collocation equations has been solved numerically using Newton Raphson method. Numerical examples have been discussed to check the reliability and efficiency of the scheme. Numerically calculated results have been compared to the exact values as well as the values already given in the literature to check the compatibility of the scheme. Error analysis has been studied by calculating the absolute error, $L_2- norm$ and $L_{\infty}- norm$. Computer codes have been prepared using MATLAB.

A two-dimensional mathematical model was developed for a porous heterogeneous catalytic fixed bed reactor. The model took into account the effect of heat generated by adsorption of reactants on the catalyst surface and heat transfer from the fluid phase to the surroundings which have a significant effect on reactor performance, especially at reactor hotspot. The developed model predicted the partial oxidation of methanol to formaldehyde on FeO/MoO3 catalyst, a complex reaction system. Excellent agreement was achieved when the resultant simulated results were compared with experimental data in the literature. The proposed model predicted the location of the hotspot at a dimensionless distance of 0.4413 (= 0.0309 m) the same as the experiment value but with a temperature of 619 K compared with an experimental value of 622 K. The conventional heterogeneous and pseudo-homogeneous models predicted the hotspot temperature to be about 8 K and 34 K lower than the experimental value respectively.