Symmetric marching technique for the numerical solution of nonseparable elliptic equations (Q1063407)

We develop two methods for nonseparable elliptic equations of type \(\nabla \cdot (a\nabla u)=f\), based on the extension of the symmetric marching technique developed by the second author [Symmetric marching technique for elliptic boundary value problems. Thesis, I. I. T. Kanpur (1980)]. In method I, symmetric marching is applied to carry out the iterations in the iterative scheme developed by \textit{P. Concus} and \textit{G. H. Golub} [SIAM J. Numer. Anal. 10, 1103-1120 (1973; Zbl 0245.65043)]. Method II is a noniterative method based on the direct extension of symmetric marching to the above problem. Numerical results are given to illustrate the behavior of the two methods.