Hermitian Methods for the Approximate Solution of Partial Differential Equations

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General procedures, which are based on the use of Hermitian functions and employ a scheme of Hermitian collocation, are given for the approximate solution of partial differential equations. This procedure is extended, by utilizing local approximations of the function set, to a form of localized Hermitian collocation. For a particular class of Hermitian functions and subsequent local approximations, the increases in numerical accuracy over conventional Lagrangian difference techniques are illustrated with reference to the non-homogeneous biharmonic equation. Where iterative solution procedures are employed this increased numerical accuracy is achieved, at least for the example given, with a decrease in total computational effort.