A simple and non-iterative numerical approach for solving high-order nonlinear ODEs
Although there are many numerical solution approaches to ordinary differential equations (ODEs) in the literature, very few are effective in solving non-linear ODEs, particularly when they are of order higher than one. With the modern symbolic calculation packages, such as Maple and Mathematica, being readily available in scientific research and engineering calculations, a new numerical method based on the repeated use of a symbolic calculation package is presented in this talk. Our method is particularly suitable for solving high-order nonlinear ODEs arising from initial value problems. One important feature of our approach is that there is no iteration required in the time marching process.