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| In this paper, the Legendre-tau spectral method is applied tothe initial value problem of nonlinear ordinary differential equations,and the nonlinear term is interpolated at the Legendre-Gauss-Lobatto point.A simple iterative format is used for computation.Under the local Lipschitz condition, the $L^2$-error estimates of the iterative solutionand the exact solution are given,and the optimal order is obtained in terms of spectral approximation.For long-time computation,the multi-interval scheme of the above method is established,and the corresponding $L^2$-error estimate is obtained.The above methodology can also be applied in numerical analysis ofspace-time spectral methods for some nonlinear evolution equations.Numerical examples are given to confirm the theoretical results. |
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| Keywords:Nonlinear ordinary differential equations; local Lipschitz condition; error estimate;optimal order; Legendre-tau spectral method |
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