Experimental investigation of the block method for the Laplace equation on polygons (Q1571247)

The real characteristics of the block method are investigated as applied to the numerical solution of two special boundary value problems. The Dirichlet problem is solved on a square with a cut when the perturbation is concentrated at the end of the cut, and a modified mixed boundary value problem involving an unknown parameter and subject to an additional nonlocal condition is solved on a trapezium. Experimental investigations exhibit the fast convergence of the approximate solution and prove the stability of the method with respect to roundoff errors.