Pseudospectral meshless radial point interpolation for generalized biharmonic equation in the presence of Cahn–Hilliard conditions

In this study, we develop an approximate formulation for a generalization form of biharmonic problem based on pseudospectral meshless radial point interpolation (PSMRPI). The boundary conditions are considered as Cahn–Hilliard type boundary conditions with application to spinodal decomposition. Since the rigorous steps to analyze such a problem is of high-order derivatives, implementing multiple boundary conditions and especially when the geometry of domain of the problem is complex. In PSMRPI method, the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high-order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. Furthermore, it is observed that the multiple boundary conditions can be imposed by an erudite application of PSMRPI on nodal points near the boundaries of the domain. The main results of generalized biharmonic problem are demonstrated by some examples to show validity and trustworthy of PSMRPI technique.