New methods of deriving more accurate difference equations are given. These are used to compute the stresses in thin shells. The governing shell equations are derived making the Donnell assumptions, so that unknowns are expressed in changes of curvatures and normal forces. These equations are then solved using improved finite difference formulas in which terms of higher order, compared to ordinary finite difference formulas, are taken into account. Several examples are given showing results comparable to other methods but using far fewer unknowns.

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