Using Chebyshev polynomials zeros as point grid for numerical solution of linear and nonlinear PDEs by dierential 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 non- linear Partial Dierential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Dier- ential Quadrature (DQ) method- based RBFs are applied to nd the numerical solution of the linear and nonlinear PDEs. The multiquadric (MQ) RBFs as basis function will introduce and applied to discretize PDEs. Dierential quadrature will introduce brie y 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.