A Highly Accurate MCTM for Direct and Inverse Problems of Biharmonic Equation in Arbitrary Plane Domains

Abstract: Trefftz method (TM) is one of widely used meshless numerical methods in el-liptic type boundary value problems, of which the approximate solution is expressed as a lin-ear combination of T-complete bases, and the un-known coefficients are determined from bound-ary conditions by solving a linear equations sys-tem. However, the accuracy of TM is severely limited by its ill-conditioning. This paper is a con-tinuation of the work of Liu (2007a). The col-location TM is modified and applied to the di-rect and inverse problems of biharmonic equation in a simply connected plane domain. Due to its well-conditioning of the resulting linear equations system, the present modified collocation Trefftz method (MCTM) can effectively solve the inverse problems without needing of overspecified data, iteration, and regularization. So that, the compu-tational cost of MCTM is saving. Numerical ex-amples show the effectiveness of the new method in providing highly accurate numerical solutions even subjecting to large noise of the given bound-ary data