New version of line-by-line recursive method for solving a difference elliptical equations

We consider a new version of the closure equation for the line-by-line recursive method. The equation is a double-point linear connection of the desired solution’s values in the neighboring nodes of the area grid. A special feature of the considered closure is asymptotically exact value of the equation factors in the case when the solution converges. Higher efficiency of the discussed version of the line-by-line recursive method for solving systems of linear algebraic equations with ill-conditioned matrices as compared with its previous versions is demonstrated by examples of model problem solutions.