Pseudospectral meshless radial point interpolation for generalized biharmonic equation subject to simply supported and clamped boundary conditions

A new high-order nine-point stencil, based on integrated-RBF approximations, for the first biharmonic equation

“…Numerically solving the first biharmonic equation faces some significant challenges, namely the approximation of high-order derivatives and cross derivatives, and the imposition of double boundary conditions. Various numerical schemes have been developed, e.g., [1,2,3,4,5,6,7]. In the context of finite difference methods [1], the standard 13-point stencil with truncation error of O(h 2 ) and the 25-point (5 × 5) approximation with truncation error of O(h 4 ) are obtained, where some grid points outside the problem domain are required.…”