, Volume 2, Issue 1, pp 61-64

Note on the solution of a certain boundary-value problem

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Abstract

A simple algorithm is described for inverting the operatorD x D y (D x andD y here and subsequently denote partial differentiation with respect tox andy respectively) which occurs in the iterative solution of the equationD x D y f (x, y)=g (x, y, f, D x f, D x 2 f,D x D y f, D y 2 f) when boundary values off(x,y) are given along the sides of the rectangle in thexy-plane whose corners are at the points (a,b); (a+(n+1)k,b); (a+(n+1)k,b+(n+1)h); (a,b+(n+1)h).

Communication M. R. 43 of the Computation Department of the Mathematical Centre, Amsterdam.