ANALYSIS OF THE MIXED BOUNDARY VALUE PROBLEM FOR THE POISSON’S EQUATION

The mixed boundary value problem for the Poisson’s equation is examined in a bounded flat domain. continued variational form through with Dirichlet condition to rectangular To solve problem, modified method of fictitious components formulated. considered on finite-dimensional space. previous space matrix form, known considered. It shown that absolute error energy norm converges speed geometric progression. generalize components, new version iterative extensions proposed. solved using extensions. proposed extensions, relative stronger than progression rate. parameters specified are selected minimum residual method. conditions which sufficient convergence applied process indicated. An algorithm implements written. In this algorithm, an automated selection conducted, and stopping criterion established when achieving estimate required accuracy. example application solving particular given. calculations, set. However, errors obtained numerical solution original other ways. For example, grid nodes calculated pointwise. achieve no more few percent, just iterations required. Computational experiments confirm asymptotic optimality theory.