A Multi-Domain Legendre Spectral Collocation Method For Nonlinear Neutral Equations With Piecewise Continuous Argument

In this paper, for the neutral equations with piecewise continuous argument, we construct a spectral collocation method by combining the shifted Legendre-Gauss-Radau interpolation and a multi-domain division. Based on the non-classical Lipschitz condition, the convergence results of the method are derived. The results show that the method can arrive at high accuracy under the suitable conditions. Several numerical examples further illustrate the obtained theoretical results and the computational effectiveness of the method.