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In this paper, we propose a quasi boundary value method for an homogeneous biharmonic equation in a rectangular domain. It is known that the problem for the Biharmonic equations is severely ill-posed in the sense of Hadamard [12], i.e., the solution does not depend continuously on the given data. Convergence estimates for the regularized solutions are obtained under a priori and a posteriori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Meshless method choosing Heaviside step function as a test function for solving simply supported thin plates under various loads is presented in this paper. The shape functions using regular and irregular nodal distribution as well as order of polynomial basis choice are constructed by moving kriging interpolation. Alternatively, two-field-variable local weak forms are used in order to decompose the governing equation, biharmonic equation, into a couple of Poisson equations and then impose straightforward boundary conditions. Selected numerical examples are considered to examine the applicability, the easiness, and the accuracy of the proposed method. Comparing to an exact solution, this robust method gives significantly accurate numerical results, implementing by maximum relative error and root mean square relative error. [ABSTRACT FROM AUTHOR]