Multiscale localized differential quadrature method using cell approach for solving differential equation with large localized gradient

Abstract

The traditional differential quadrature (DQ) method is used to approximate derivatives and its application is limited to the number of grid points. In this paper, a multiscale localized differential quadrature (MLDQ) method was developed by increasing the number of grid points in critical region, and approximating the derivatives at the certain grid point which selected. This present method applied in twodimensional differential equation, together with the fourthorder Runge-Kutta (RK) method. Numerical examples are provided to validate the MLDQ method. The obtained results by this method are high accuracy and good convergence comparing with the other conventional numerical methods such as finite difference (FD) method.