Numerical approach for solving diffusion problems using cubic B-spline collocation method

A numerical approach for modeling the removal of homogeneous solutes from the porous structure is presented. Pore diffusion equations, controlling the overall process, are expressed in terms of concentration of solute as a function of position in bed and washing period. A computational scheme, specifying knot vector(s) and control points (de Boor points), to solve diffusion model using cubic B-spline collocation method (CSCM) is given. The knot vector provides sufficient resolution and control points yield an accurate approximation of the desired curve. Convergence of numerical scheme is of O(h2)O(h2). Four problems have been worked out by the proposed scheme. Results are plotted graphically for fairly wide range of parameters. A comparison with the previous techniques demonstrates the superiority of the proposed method on basis of computational time, efficiency and accuracy.

► CSCM eliminates continuity condition of trial function and first derivative.
► Faster results with less memory storage are achieved by CSCM.
► For wide range of parameter Pe exact and numerical results are in good agreement.
► The proposed method is uniformly convergent of order almost two.