The finite difference methods and their extrapolation for solving biharmonic equations (Q2917646)

The authors consider the two dimensional biharmonic Poisson equation with non-homogeneous boundary conditions. Existence and convergence of the finite difference methods solutions are obtained by estimating the lower bounds of the minimum eigenvalues of the discrete matrix and making use of the Taylor series, respectively. The accuracy is proved to be of order \(O(h^{2})\). Moreover, the extrapolation techniques based on asymptotic expansion of the errors are used to improve the high accuracy of the solutions.