相关论文: On the fourth-order accurate compact ADI scheme fo…
In this paper, based on the developed nonlinear fourth-order operator and method of order reduction, a novel fourth-order compact difference scheme is constructed for the mixed-type time-fractional Burgers' equation, from which…
Based on our recent results, in this paper, a compact finite difference scheme is derived for a time fractional differential equation subject to the Neumann boundary conditions. The proposed scheme is second order accurate in time and…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating…
In the paper, a newly developed three-point fourth-order compact operator is utilized to construct an efficient compact finite difference scheme for the Benjamin-Bona-Mahony-Burgers' (BBMB) equation. Detailed derivation is carried out based…
In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes are fourth order accurate in space and second…
We present new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with mixed derivative terms. Our approach is based on the…
In this paper, a high-order exponential scheme is developed to solve the 1D unsteady convection-diffusion equation with Neumann boundary conditions. The present method applies fourth-order compact exponential difference scheme in spatial…
This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier-Stokes equations in two- and three-dimensional curvilinear domains. The higher-order…
In this paper, by introducing two temporal-derivative-dependent auxiliary variables, a linearized and decoupled fourth-order compact finite difference method is developed and analyzed for the nonlinear coupled bacterial systems. The…
We show that the classical fourth order accurate compact finite difference scheme with high order strong stability preserving time discretizations for convection diffusion problems satisfies a weak monotonicity property, which implies that…
In this paper, by using Strang's second-order splitting method, the numerical procedure for the three-dimensional (3D) space fractional Allen-Cahn equation can be divided into three steps. The first and third steps involve an ordinary…
In this paper, efficient alternating direction implicit (ADI) schemes are proposed to solve three-dimensional heat equations with irregular boundaries and interfaces. Starting from the well-known Douglas-Gunn ADI scheme, a modified ADI…
This paper presents an efficient high-order sharp-interface method for solving the three-dimensional (3D) Poisson equation with Dirichlet boundary conditions on a nonuniform Cartesian grid with irregular domain boundaries. The new approach…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of…
In this paper, an efficient and high-order accuracy finite difference method is proposed for solving multidimensional nonlinear Burgers' equation. The third-order three stage Runge-Kutta total variation diminishing (TVD) scheme is employed…
In this paper, a second-order backward difference formula (abbr. BDF2) is used to approximate first-order time partial derivative, the Riesz fractional derivatives are approximated by fourth-order compact operators, a class of new…
A numerical scheme based on backward differentiation formula (BDF) and generalized differential quadrature method (GDQM) has been developed. The proposed scheme has been employed to investigate three cases of Burgers equation,…
This work proposes an efficient space-time two-grid compact difference (ST-TGCD) scheme for solving the two-dimensional (2D) viscous Burgers' equation subject to initial and periodic boundary conditions. The proposed approach combines a…