## The mechanical quadrature methods and their extrapolation for solving BIE of Steklov eigenvalue problems.(English)Zbl 1069.65123

Authors’ abstract: By means of potential theory Steklov eigenvalue problems are transformed into general eigenvalue problems of boundary integral equations (BIE) with logarithmic singularity. The paper presents quadrature methods for BIE of the Steklov eigenvalue problem, which possess high accuracies $$O(h^3)$$ and low computing complexities. Asymptotic expansion of the errors with odd powers is shown. Using $$h^3$$-Richardson extrapolation, the authors not only improve the accuracy order of approximations, but also derive a posteriori estimate and adaptive algorithms. The efficiency of the algorithm is illustrated on some examples.

### MSC:

 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65N38 Boundary element methods for boundary value problems involving PDEs 35P15 Estimates of eigenvalues in context of PDEs 65N15 Error bounds for boundary value problems involving PDEs