Evaluation of Multi-Order Derivatives by Local Radial Basis Function Differential Quadrature Method

Abstract

AbstractIt is difficult to obtain the derivative values from most mesh dependent numerical procedures in general. This study proposes an efficient computational tool to accurately evaluate the multi-order derivatives by the radial basis functions and local differential quadrature (LRBF-DQ) algorithm. Most of the traditional derivative calculations can be only adopted to evaluate the differential values with the regular meshes. Moreover, the traditional numerical schemes are very restricted by the order of the shape functions. The present technique can be applied to both the structured and unstructured meshes as well as meshless numerical algorithms – such as RBFs and LDQ method. In addition, the proposed model can be also used to estimate multi-order or mixed partial derivative values because its test function using RBFs is a multi-order differentiable function. All of the evaluation of derivative results will be compared with the exact solutions and other numerical techniques. Consequently, this study provides an effective algorithm of post process to accurately calculate the multi-order derivative values for any numerical schemes.