An efficient scheme for numerical solution of Burgers' equation using quintic Hermite interpolating polynomials

A numerical scheme combining the features of quintic Hermite interpolating polynomials and orthogonal collocation method has been presented to solve the well-known non-linear Burgers' equation. The quintic Hermite collocation method (QHCM) solves the non-linear Burgers' equation directly without converting it into linear form using Hopf-Cole transformation. Stability of the QHCM has been checked using Eucledian and Supremum norms. Numerical values obtained from QHCM are compared with the values obtained from other techniques such as orthogonal collocation method, orthogonal collocation on finite elements and pdepe solver. Numerical values have been plotted using plane and surface plots to demonstrate the results graphically.