A method for global approximation of the solution of second order IVPs

Abstract

For the numerical solution of the second order initial value problem, a family of global methods is derived by finding Galerkin approximations on a given interval. For each n ≥ 1 a method is defined that uses a particular inner product in the Galerkin equation. The methods are symmetric collocation on the zeros of Chebyshev polynomials of the second kind and are related to implicit Runge-Kutta-Nyström methods. Order, stability and error analysis are here studied. Numerical examples provide favorable comparisons with other existing methods.

Keywords

• initial value problem
• chebyshev series