We present a novel implicit scheme for the numerical solution of time-dependent conservation laws. The core idea presented method is to exploit and approximate mixed spatial-temporal derivative that occurs naturally when deriving some second order accurate schemes in time. Such an approach introduced context Lax-Wendroff (or Cauchy-Kowalevski) procedure time not completely replaced by space der...

a nonstandard finite difference (nsfd) scheme has been constructed and analyzed for a mathematical model that describes lotka–volterra food web model. this new discrete system has the same stability properties as the continuous model and,on the whole, it preservesthe same local asymptotic stability properties. linearized stability theory and schur–cohn criteria are used for local asymptoticstab...

In this paper, we resolve the ever-present confusion over QUICK scheme: it is a second-order scheme or third-order scheme. The scheme, as proposed in original reference [B. P. Leonard, Comput. Methods. Appl. Mech. Eng., 19, (1979), 59-98], (not second-order) finite-volume for integral form of general nonlinear conservation law with point-valued solutions stored at cell centers numerical solutio...