Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
483632 | Journal of the Egyptian Mathematical Society | 2012 | 5 Pages |
In this paper, we use a hybrid method based on a variant of Trefftz’s method (TM), in combination with the usual Boundary Collocation Method (BCM) to find the approximate solution to a singular, two-dimensional mixed boundary-value problem for Laplace’s equation in a rectangular sheet with one curved side.After expressing the solution as a finite linear combination of harmonic trial functions, the usual BCM is used to enforce the boundary condition on the curved side, while a variant of TM is applied to the three remaining sides. The singularity at one corner of the rectangle is treated via the enrichment of the expansion with a specially built harmonic function which has a singularity at one corner.The procedure ultimately produces a rectangular set of linear algebraic equations, which is solved by QR factorization method.Numerical results are presented and discussed, in order to assess the efficiency of the proposed method.