In this paper, we use some numerical methods namely Lax-Wendroff (LW), two-step Lax-
Friedrichs (LF), two variants of composite methods made up of Lax-Wendroff and the twostep
Lax-Friedrichs and Fromm’s scheme to solve a 1D linear advection and 1D diffusionless
Burger’s equation, at some values of the Courant number. We then use two optimisation
techniques based on both dispersion and dissipation and two optimisation techniques based
on only dispersion and obtain the variation of the integrated errors vs the CFL number. It
is seen that out of the five techniques, only one is a good measure of the shock-capturing
of property of numerical methods.