On compact difference schemes for the heat equation (Q1395198)

The authors construct and analyze the compact finite-difference equations, as well as their three-dimensional analogues, for the Dirichlet initial-boundary value problem for the following anisotropic heat equation with convection \(\mu\frac{du}{dt}=\frac{d}{dx}p\frac{du}{dx}-a\frac{du}{dx}+\frac{d}{dy}q\frac{du}{dy}-b\frac{du}{dy}+f(x,y.t)\), \(0<t<T\), \((x,y)\in\Omega\) is a rectangle. The input data are assumed to guarantee the smoothness of \(u(x,y,t)\).