Hermite type radial basis function-based differential quadrature method for higher order equations

Abstract

In the paper, the radial basis function-based differential quadrature method (RBF-DQM) that uses Hermite type interpolation is developed. The method is an extension of the known RBF-DQM, which is a meshless numerical technique for solving differential equations. According to this technique, derivatives in a governing equation are approximated by a linear weighted sum of the sought function values defined at scattered nodes. To allow the method to be applied in higher order equations, where more than one boundary condition is imposed at an edge, Hermite type interpolation for the radial basis functions is used and appropriate weighting coefficients for differential quadrature method are determined in the paper. As a numerical test the method is used to discretize the governing equation for the free vibration of thin plates with various boundary conditions. Different shaped plates with various boundary conditions are analyzed. The convergence tests carried out in the work confirm usefulness of the method as a truly meshless technique.