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“…of almost four using quadratic basis functions, thus leading to superconvergence. Note that the numerical program developed by the third author (see [39]) is an extension of BIEPACK (boundary integral equation package for the solution of integral equations of the second kind arising from the Laplace equation) developed by Atkinson (see [5]) which has been recently used in a variety of problems dealing with the Helmholtz equation (see [35,40,41,42,43,44] among others).…”

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“…of almost four using quadratic basis functions, thus leading to superconvergence. Note that the numerical program developed by the third author (see [39]) is an extension of BIEPACK (boundary integral equation package for the solution of integral equations of the second kind arising from the Laplace equation) developed by Atkinson (see [5]) which has been recently used in a variety of problems dealing with the Helmholtz equation (see [35,40,41,42,43,44] among others).…”

“…In this section, we explain how to discretize (6) using quadratic interpolation of the boundary, but using piecewise quadratic interpolation with α = (1 − 3/5)/2 (see [22] for the 3D case) instead of quadratic interpolation for the unknown u on each of the n f boundary elements which ultimately leads to the non-linear eigenvalue…”

“…Standard convergence results are available for boundary integral equations of the second kind using boundary element collocation method under suitable assumptions on the boundary (for example the boundary is at least of class C 2 ) and the boundary condition for the Laplace equation (see [5]). Quadratic approximations of the boundary and the boundary function yield cubic convergence (refer to [5] for the Laplace equation and [22] for the Helmholtz equation). In fact, the convergence results can be improved as shown in [22] for the threedimensional case.…”