SEAN O. SETTLE, CRAIG C. DOUGLAS, IMBUNM KIM, DONGWOO SHEEN, ON THE DERIVATION OF HIGHEST-ORDER COMPACT FINITE DIFFERENCE SCHEMES FOR THE ONE- AND TWO-DIMENSIONAL POISSON EQUATION WITH DIRICHLET ...

Mimetic Schemes: Finite difference approaches designed to replicate key mathematical identities, ensuring conservation and consistency across both interior and boundary discretisations.

We study the stability of finite difference schemes for hyperbolic initial boundary value problems in one space dimension. Assuming l 2 -stability for the discretization of the hyperbolic operator as ...

The numerical experiments reveal that the proposed scheme outperforms the standard second-order finite-difference scheme in terms of accuracy versus runtime and shows an unconditionally stable ...

Abstract ABSTRACT In this paper we investigate the effectiveness of alternating direction implicit (ADI) time-discretization schemes in the numerical solution of the three-dimensional ...