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.

在这项研究中，我们基于伪谱无网格径向点插值（PSMRPI），为双谐波问题的广义形式开发了近似公式。边界条件被认为是Cahn–Hilliard类型边界条件，适用于旋节线分解。由于分析此类问题的严格步骤是高阶导数，因此应实现多个边界条件，尤其是当问题域的几何形状复杂时。在PSMRPI方法中，节点不需要规则分布，甚至可以是任意的。通过构造运算矩阵，很容易就结点的值获得未知数的高阶导数。此外，可以观察到，可以通过对域边界附近的节点上PSMRPI的博学应用来施加多个边界条件。通过一些实例证明了广义双谐波问题的主要结果，以证明PSMRPI技术的有效性和可信赖性。