A third-order accurate variation nonexpansive difference scheme for single nonlinear conservation laws

It was widely believed that all variation nonexpansive finite difference schemes for single conservation laws must reduce to first-order at extreme points of the approximation. It is shown here that this belief is in fact false. A third-order scheme, which at worst may reduce to second order at extreme points, is developed and analyzed. Moreover, extensive numerical experiments indicate that the third-order scheme introduced here yields superior approximations when compared with other variation nonexpansive difference schemes.