A numerical method for the solution of the elliptic MongeAmpère Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation (OT) problem is presented. A local representation of the OT boundary conditions is combined with a finite difference scheme for the Monge-Ampère equation. Newton’s method is implemented leading to a fast solver, comparable to solving...

Numerical Simulation of three dimensional wave equation is conducted in a cubic domain which contains two parts, part A and part B. Part A of the domain is a I -shaped empty channel, containing air, and part B, containing a solid medium, is the difference between the whole cubic domain and part A. A Dirichlet type boundary condition is specified at the inlet boundary. At all other boundaries of...

American put options with the regime-switching model is a system of coupled free boundary problems. In this study, we present an accurate finite difference method Hermite interpolation for solving system. To end, first employ logarithmic transformation to map each regime fixed interval and then eliminate first-order derivatives in transformed by taking obtain partial differential equations whic...

The elliptic interface problems with discontinuous and high-contrast coefficients appear in many applications often lead to huge condition numbers of the corresponding linear systems. Thus, it is highly desired construct high order schemes solve coefficients. Let ? be a smooth curve inside rectangular region ?. In this paper, we consider problem ??·(a?u)=f ??? Dirichlet boundary conditions, whe...

A high-order finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme a new second-order discretization, which is based on Crank-Nicholson method, is applied for the time fractional part and fourth-order accuracy compact approximation is applied for the second-order space d...

Abstract: In this paper, a comparison between h ig h e r order schemes has been performed in terms of numerical accuracy. Four finite difference schemes, the e xp lic it fourth-order compact Pade scheme, the implicit fourth-order Pade scheme, flowfield dependent variation (FDV) meth o d a n d h igh order compact flowfie ld dependent variation (HOC-FDV) scheme are tes ted. The FDV scheme is used...

Based on the developed thirdand fourth-order upwind compact finite difference(FD) schemes, a new high-order weighted upwind FD approach, which is called combined compact upwind FD method, is proposed for decreasing dispersive(phase) and dissipative errors of the finite difference approximations. The newly proposed combined compact upwind FD schemes have the characters of group velocity control ...

We present a sixth order explicit compact finite difference scheme to solve the three dimensional (3D) convection diffusion equation. We first use multiscale multigrid method to solve the linear systems arising from a 19-point fourth order discretization scheme to compute the fourth order solutions on both the coarse grid and the fine grid. Then an operator based interpolation scheme combined w...

In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has thes...