Solution of Benjamin-Bona-Mahony-Burgers equation using collocation method with quintic Hermite splines

Abstract

In this paper, a hybrid numerical technique is developed to solve the Benjamin-Bona-Mahony-Burgers (BBMB) equation. This technique involves the application of quintic Hermite collocation method (QHCM) and weighted finite difference scheme. The discretization of BBMB equation is done using collocation method with Hermite splines of order five along spatial direction and using weighted finite difference scheme along temporal direction. The nonlinear equation is discretized without using the Hopf-Cole transformation. Stability of the proposed technique using Von-Neumann method is checked. Convergence analysis of the technique is also done in detail. Validity of the technique is shown by solving four test examples with different boundary and initial conditions. The calculated results are found to be in good agreement with the exact solutions and are better than the results from other techniques given in the literature.