An optimal B-spline collocation technique for numerical simulation of viscous coupled Burgers’ equation

In this paper, an optimal cubic B-spline collocation method is applied to solve the viscous coupled Burgers’ equation, which helps in modeling the polydispersive sedimentation. As it is not possible to obtain optimal order of convergence with the standard collocation method, so to overcome this, posteriori corrections are made in cubic B-spline interpolant and its higher-order derivatives. This optimal cubic B-spline collocation method is used for space integration and for time-domain integration, the Crank-Nicolson scheme is applied along with the quasilinearization process to deal with the nonlinear terms in the equations. Von-Neumann stability analysis is carried out to discuss the stability of the technique. Few test problems are solved numerically along with the calculation of L۲, L∞ error norms as well as the order of convergence. The obtained results are compared with those available in the literature, which shows the improvement in results over the standard collocation method and many other existing techniques also.

Keywords:

Coupled Burgers’ equation , Cubic B-splines , Optimal collocation method , Crank-Nicolson scheme , Quasilinearization , Von-Neumann stability analysis