The solution for a Dirichlet problem on a given plane domain and with given boundary values is usually approximated in numerical computation by its discrete analog defined and determined on an approximating set of net points. It can be proved that the approximation thus obtained converges to the exact solution, when the net becomes denser indefinitely, independently of the domain and the boundary values subject to rather weak conditions. Nevertheless, the irregularity of the boundary curve and of the boundary values affects strongly the convergence rate. For instance, if both are analytic and if a proper boundary interpolation scheme is used, then the simplest net analog leads to an error which decreases asymptotically at least proportional to the square of the mesh constant h , as proved by Gerschgorin [2] and Collatz [1]:δ h = O ( h 2 ).

article Free Access Share on On the Solution of Poisson's Difference Equation Author: Pentti Laasonen University of California, Los Angeles and Finland Institute of Technology, Helsinki University of California, Los Angeles and Finland Institute of Technology, HelsinkiView Profile Authors Info & Claims Journal of the ACMVolume 5Issue 4Oct. 1958 pp 370–382https://doi.org/10.1145/320941.320951Published:01 October 1958Publication History 21citation659DownloadsMetricsTotal Citations21Total Downloads659Last 12 Months17Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF