Solution of Two-Point Boundary Value Problems Using Quintic Hermite Collocation Method

Abstract

The study presents an effort in solving the mathematical model of pulp washing using the quintic Hermite collocation method (QHCM) to improve the accuracy using minimum time and effort. The relevant problems having applications associated with the pulp washing phenomenon are explored with the QHCM. The present technique is found to be efficient, economical in use, takes less CPU time, and is easy to implement. Besides, the numerical results derived using the present technique are compared with the previous techniques and are found to be superior and accurate. The range of various parameters used for pulp washing based on the data collected from the industry shows that the target of efficient washing is achieved for Pe between 10 and 20. It is noticed that the concentration profile at the exit level for the range of porosity between 0.941-0.961 has not much effect on the concentration profile. Further, the results derived for the concentration of solute at the exit level are not much affected by the range between 55.88 - 81.52 of fiber consistency. It is evident from the results of the study that various parameters used by the industry are optimal. The computational cost of the model is reduced with the present technique. Therefore, the method worked well and can be widely employed to solve more problems related to the application areas of convection, advection, diffusion, and dispersion phenomena owing to its accuracy, simplicity, and less time-consuming property.