Using the Goursat representation for the biharmonic function and approximate solutions of a corrected Muskhelishvili equation we construct approximate solutions for biharmonic problems in smooth domains of $\mathbf{R}^2$. It is shown that the sequence of these approximate solutions converges uniformly on each compact subset of the initial domain $D$. Under additional conditions it converges uniformly on $D$. We also provide numerical examples.
Approximate solution of the biharmonic problem in smooth domains
VENTURINO, Ezio
2006-01-01
Abstract
Using the Goursat representation for the biharmonic function and approximate solutions of a corrected Muskhelishvili equation we construct approximate solutions for biharmonic problems in smooth domains of $\mathbf{R}^2$. It is shown that the sequence of these approximate solutions converges uniformly on each compact subset of the initial domain $D$. Under additional conditions it converges uniformly on $D$. We also provide numerical examples.
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