VARIATIONAL METHODS FOR APPROXIMATING SOLUTIONS OF DEL ² u(x) equals f(x) plus k(x)u(x) AND GENERALIZATIONS.

The iterative procedure of Guy, Sales, Brami-Depaux, and Joly-Cabaret (GSBJ) for approximately solving equations of the form DEL **2u equals f plus ku is analyzed and generalized from the viewpoint of the calculus of variations. The variational approach is tested on three simple example problems and the numerical results are seen to compare favorably with those of GSBJ and with the exact solution. In addition, two new variational functionals are derived, various iteration schemes are discussed, the method is extended to more general equations, and further connections with other work are established.