DIRECT SOLUTION OF THE BIHARMONIC EQUATION USING NONCOUPLED APPROACH

The Dirichlet problem for the biharmonic equation is solved using the thirteen-point formula. The prescribed normal derivative on the boundary is replaced by two classes of boundary approximations in order to define the solution at certain fictitious node points. A direct method is used to solve the resulting system of algebraic equations. It is found that the accuracy of the numerical solution strongly depends upon the boundary approximation used, as in the coupled-equation approach. However, the cost of obtaining the solution is almost independent of the boundary approximation, unlike the coupled-equation approach. © 1979.