The solution of hyperbolic equation with wave nature has sharp discontinuties in the medium at the wave front. Difficulties encounted in the numrtical solution of such problem in clude among oth-ers numerical oscillation and the representation of sharp discontinuities with good resolution at the wave front. In this work inviscid Burgers equation and modified heat conduction equation is intro-duced as hyperboic equation. These equations are caculated by numerical methods(explicit method MacCormack method Total Variation Diminishing(TVD) method) along various Courant numbers and numerical solutions are compared with the exact analytic solution. For inviscid Burgers equa-tion TVD method remains stable and produces high resolution at sharp wave front but for modified heat Conduction equation MacCormack method is recommmanded as numerical technique.