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In this paper, we introduce a numerical method to obtain an accurate approximate solution of the integro-differential delay equations with state-dependent bounds. The method is based basically on the generalized Mott polynomial with the parameter-   $$\beta$$   β    , Chebyshev–Lobatto collocation points and matrix structures. These matrices are gathered under a unique matrix equation and then solved algebraically, which produce the desired solution. We discuss the behavior of the solutions, controlling their parameterized form via    $$\beta$$   βand so we monitor the effectiveness of the method. We improve the obtained solutions by employing the Mott-residual error estimation. In addition to comparing the results in tables, we also illustrate the solutions in figures, which are made up of the phase plane, logarithmic and standard scales. All results indicate that the present method is simple-structured, reliable and straightforward to write a computer program module on any mathematical software.

A numerical method with a control parameter for integro-differential delay equations with state-dependent bounds via generalized Mott polynomial