Scalar boundary integral equation formulas for the biharmonic equation — numerical experiments

Abstract

We consider numerical methods of the four scalar integral equation formulas for the biharmonic equation, suggested by the author in an earlier paper. The numerical methods are fully discrete collocation methods, based on technique of singularity subtraction and the rectangular quadrature rule. The numerical methods are computationally effective for all four formulas when the domain has a smooth boundary. When the boundary has corners, mesh grading of sufficient order yields desired convergences.