ORDVAC Solutions of the Dirichlet Problem
David M. Young · Journal of the ACM · 1955
The use of finite difference methods enables one to solve numerically many boundary value problems involving partial differential equations of elliptic type for which explicit a,~alytic solutions are not available.To date these methods have primarily been used for manual computations as described for instance by Southwell, 14 Shortley and •eller, 12 Emmons, 2 Allen, 1 and Shaw 11.Anyone who has carried out the method by hand will be impressed by the large amount of drudgery which is required, and probably feels that here is a place where the use of high speed machines is indicated.However, until recently the use of machines has been largely limited to the solution of Laplace's equation in a square, as described in Snyder and Livingston, 13 Young and Lerch, 20 and Young and Warlich, 21 although, of course, other problems have been treated.**Thereason machines have not been used more is probably that, in spite of the fact that they can eliminate the drudgery of carrying out the iterations, a large amount of preparation is needed for each problem as compared with hand methods.On the other hand, manual methods are more flexible and can be quickly adapted to widely varying types of problems.In order for the automatic procedures tohave any chance of competing with manual methods, it would appear necessary to have available a large routine capable, with the insertion of constants on tape specifying the differential equation, the region, the boundary conditions, the iteratire method, etc., of solving a large class of problems.The main part of the routine would be prepared once and for all, and only a small amount *Presented at the meeting of the Association, Jtme 23-25, 1954.Thls work was done under Contract No. DA-36-034-ORD-1486, placed by the Office of Ordnance Research, U. S. Army, with the University of Maryland.**For instance more difficult problems on weather prediction have been solved at the InstitUte c~ Advanced Study.