A spectral collocation method for solving initial value problems of first order ordinary differential equations (Q612891)

The authors study a spectral collocation method for solving initial value problems of first order ordinary differential equations. They derive this new numerical process by approximating the exact solution directly by the Legendre-Gauss-Lobatto interpolation with \(N+1\) nodes. Later error estimates and a multistep version of the collocation method are presented. Finally the authors present some numerical results and compare the proposed new methods with several commonly used methods.