Abstract: It is shown that there are partial TVD regions after analyzing Lax Wendroff and Warming Beam schemes from the TVD conditions of hyperbolic equation. Based on which, new second order accurate TVD schemes of three or four grids in space are constructed in order to keep second order accuracy near the extreme points. Finally a comparative study is presented to solve linear hyperbolic equation by the new and old TVD schemes.

Key words: TVD, hyperbolic equation, finite difference scheme, second order accuaracy