The Solution of Two-Point Boundary Value Problems by the Alternating Group Explicit (AGE) Method
David John Evans, W.S. Yousif · SIAM Journal on Scientific and Statistical Computing · 1988
In this paper, a new explicit iterative solution for the finite difference equations of the two-point boundary value problem is given. In this new approach, the coefficient matrix of the obtained system is split into component matrices $G_1 $, $G_2 $, and an iterative method formulated which can be easily expressed in explicit form. Alternating this strategy on the grid points along the real axis results in the alternating group explicit (AGE) method analogous to the well-known ADI method. The convergence analysis of the new method is briefly discussed, its extension to multidimensional problems and the results of numerical experiments presented.