Solution of nonlinear initial-value problems by the spline-based differential quadrature method

The spline-based differential quadrature method (SDQM) is applied to the solution of nonlinear initial-value problems. Explicit expressions of weighting coefficients for approximation of derivatives are presented. Dynamic systems with Duffing-type nonlinearity are solved to demonstrate the effectiveness of the method. Numerical results of three examples show that the spline-based differential quadrature method is versatile and stable in the solution of nonlinear initial-value problems. It can be counted on to achieve satisfactory accuracy for long-term integration.