A stable high order finite difference with a fully implicit time-marching scheme is proposed to solve the two-dimensional unsteady convection diffusion equation with variable coefficients. It is essentially compact and has the nice features of a compact scheme with regard to the treatment of boundary conditions. A time-dependent multigrid full approximation storage(FAS) scheme , which is suitab...

In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic propagation through heterogeneous media with variable density velocity. The fourth-order accuracy space second-order time. compactness obtained by so-called combined method, utiliz...

We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and secondorder accurate in time for vanishing correlation. In our numerical study we obtain highorder numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all ...

Existence and mutiplicity of solutions to elliptic equations of fourth order on compact manifolds. Abstract. This paper deals with a fourth order elliptic equation on compact Riemannian manifolds.We establish the existence of solutions to the equation with critical Sobolev growth which is the subject of the first theorem. In the second one, we prove the multiplicity of solutions in the subcriti...

In this paper, we present an approach to deal with the dynamics of Dirac equation time-dependent electromagnetic potentials using fourth-order compact time-splitting method ($S_\text{4c}$). To purpose, time-ordering technique for Hamiltonians is introduced, so that influence time-dependence could be limited certain steps which are easy treat. Actually, in case equation, it turns out only those ...