In this paper, a non-overlapping second-order domain decomposition method for solving three-dimensional hyperbolic partial differential equation is proposed. Unconditional stability of the algorithm is analyzed. Numerical experiments show that the method is stable and very efficient. Mathematics Subject Classification: 65M06, 65M55

We investigate the stability of a temporal discretization of interface terms in grid overlapping methods. A matrix stability analysis is performed on a model problem of the one-dimensional diffusion equation on overlapping grids. The scheme stability is first analyzed theoretically, and a proof of the unconditional stability of the first-order interface extrapolation scheme with the firstand se...

A fourth order accurate discretization in time and space for the wave equation in first order system formulation is investigated. The unconditional stability of the scheme is established and the performance of the scheme is compared to a second order accurate scheme for a smooth one dimensional problem and it is also applied to a two dimensional problem with piecewise constant coefficients.

A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier–Stokes equations is formulated and analyzed. We prove unconditional stability of proposed scheme. Convergence discrete velocity established by deriving a priori error estimates. Numerical results verify convergence rates.

A novel Douglas alternating direction implicit (ADI) method is proposed in this work to solve a two-dimensional (2D) heat equation with interfaces. The ADI scheme is a powerful finite difference method for solving parabolic equations, due to its unconditional stability and high efficiency. However, it suffers from a serious accuracy reduction in space for interface problems with different mater...

In this paper we devise a first-order-in-time, second-order-in-space, convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation. The unconditional unique solvability, energy stability and ∞(0, T ; 4) stability of the scheme are established. Using the a-priori stabilities, we prove error estimates for our scheme, in both the ∞(0, T ; 2) and ∞(0, T ; ∞) norms. The proofs of these e...

A new methodology is introduced for the numerical solution of Partial Differential Equations in general spatial domains. The methodology is based on the use of the well-known Alternating Direction Implicit (ADI) approach of Peaceman and Rachford in conjunction with one-dimensional and high-order accurate Fourier representations of non-periodic data, obtained by way of a certain “continuation me...

A new Peaceman–Rachford alternating direction implicit (PR-ADI) method is proposed in this work for solving two-dimensional (2D) parabolic interface problems with discontinuous solutions. The classical ADI schemes are known to be inaccurate for handling interfaces. This motivates the development of a matched Douglas ADI (D-ADI) method in the literature, in which the finite difference is locally...