Abstract
An integral equation method for the Dirichlet problem for the biharmonic equation is proposed. It leads to a $2 \times 2$ matrix integral equation system. By taking suitable norms on the spaces of density functions, the Fredholm operator theory can be used to prove the solvability. The kernels in this system are relatively complicated. Therefore, especially when a high-order polynomial approximation is used for a numerical purpose, it is costly to evaluate the integrals that appear in the numerical system. A discrete Galerkin method that has shown superb convergence is proposed here, as in [K. Atkinson, J. Integral Equations Appl., 1 (1988), pp. 343–363] and elsewhere. When the boundary functions are smooth, exponential convergence is observed.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
