Using Chebyshev polynomial’s zeros as point grid for numerical solution of nonlinear PDEs by differential quadrature- based radial basis functions

Abstract

Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are applied to find the numerical solution of the linear and nonlinear PDEs. The multiquadric (MQ) RBFs as basis function will introduce and applied to discretize PDEs. Differential quadrature will introduce briefly and then we obtain the numerical solution of the PDEs. DQ is a numerical method for approximate and discretized partial derivatives of solution function. The key idea in DQ method is that any derivatives of unknown solution function at a mesh point can be approximated by weighted linear sum of all the functional values along a mesh line.