A Legendre–Gauss–Radau spectral collocation method for first order nonlinear delay differential equations

In this paper, we introduce a single-step Legendre–Gauss–Radau spectral collocation method for solving the first order nonlinear delay differential equations with variable delay, and analyze its convergence. We also propose two fast and efficient algorithms for the single-step scheme and apply them to the multiple interval case. Numerical results show that the suggested algorithms enjoy high order accuracy.

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