A quintic B-spline finite elements scheme for the KdVB equation Original Research Article

An algorithm for solving the Korteweg de–vries Burgersʹ (KdVB) equation, based on the collocation method with quintic B-spline finite elements is set up to simulate the solutions of the KdV, Burgersʹ and the KdVB equations. The migration of solitary waves and temporal evolution of a Maxwellian initial pulse are studied for the KdV equation. Burgersʹ equation is solved for different values of Reynolds number. The time evaluation of the solutions of the KdVB equation with different values for the diffusion and dispersion coefficients is studied. Invariants and error norms are studied wherever possible to determine the conservation properties of the algorithm. A linear stability analysis shows the scheme to be unconditionally stable.