Second-order Difference Scheme Research Articles

Three-dimensional second-order accurate difference schemes for discontinuous hydrodynamic flows

In this paper, we show how a second-order accurate two-step method used in the numerical computation of hydrodynamic flows may be derived directly from the integral conservation laws. A necessary and sufficient condition for stability for the linearized equations is derived for the three-dimensional Cartesian coordinate case.

The numerical solution of interior stationary problems of electrodynamics

WE SHALL be concerned in this paper with aspects of the numerical solution of non-self-conjugate boundary value problems such as occur when determining electric current or temperature fields in a medium with anisotropic electrical and thermal conductivity [1]. By using a variational approach we are able to carry over the most important properties of the operator of the initial problem to the approximating difference operator. We devise a divergent second-order difference scheme for the divergent positive-definite operator of the initial boundary value problem. The scheme has been employed for the numerical solution of a number of concrete physical problems.