Abstract：Since the direct collocation method has low solution accuracy on the boundary when solving boundary value problems, this paper proposes a Hermite Gradient Reproducing Kernel Collocation Method (HGCM) to improve the boundary solution accuracy. Reproducing kernel approximation is a commonly used approximation function in meshfree methods, but calculation of the high gradients is complex and time-consuming. HGCM adopts the gradient reproducing kernel functions to create any high-order derivatives of the approximation function. This improves the computational efficiency. The discrete equation is constructed by the Hermite collocation method, which improves the boundary solution accuracy. This method has high accuracy and high computational efficiency in solving the static problems of functionally graded material plates which is governed by a fourth-order partial differential equation of variant coefficients. The proposed method can be further applied to boundary value problems described by high-order partial differential equations.
2022, Vol. 43 
