Splitting extrapolation algorithms for solving the boundary integral equations of Steklov problems on polygons by mechanical quadrature methods

By the potential theory, Steklov eigenvalue problems are converted into boundary integral equations (BIEs). The singularities at corners and in the integral kernels are studied in this paper. Mechanical quadrature methods (MQMs) are presented to obtain approximations with a high accuracy order O ( h 3 ) . Moreover, the mechanical quadrature methods are simple without any singularly integral computation. Since the asymptotic expansions of the errors with the power O ( h 3 ) are shown, the high accuracy order O ( h 5 ) can be achieved for the solutions by using the splitting extrapolation algorithms (SEAs). A posteriori error estimate can also be obtained for self-adaptive algorithms. The efficiency of the algorithms is illustrated by examples.