New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method

摘要

A new algorithm for solving the general nonlinear third-order differentialequation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shiftedJacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstratethe validity and applicability of the proposed algorithm, and some comparisons are made with theexisting results. The method is easy to implement and yields very accurate results.