Improved finite difference formulas for boundary value problems

Description

This paper deals with the numerical solution of linear differential equations of fourth order by finite differences. It points out significant (but usually overlooked) errors which result from the conventional method of imposing the boundary conditions in such problems. Revised finite difference formulas are derived which apply near the boundaries and which eliminate the above errors. Three commonly encountered boundary conditions are considered. These correspond, in the terminology of beam analysis, to a clamped end, to a simply supported end and to a free end. The improvement in accuracy that can be achieved with the revised formulas is illustrated by two representative examples. The revised formulas are shown to reduce the overall error of the numerical solution by a factor of about five in a typical case. (Author)

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