# Note on the solution of a certain boundary-value problem

## Abstract

A simple algorithm is described for inverting the operator*D*_{x}*D*_{y} (*D*_{x} and*D*_{y} here and subsequently denote partial differentiation with respect to*x* and*y* respectively) which occurs in the iterative solution of the equation*D*_{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 of*f*(*x,y*) are given along the sides of the rectangle in the*xy*-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*).

## Copyright information

© BIT Foundations 1962