<p>In this study, we present a detailed operational implementation of the Tau method for approximating solutions to functional differential equations, including but not limited to delay differential equations and pantograph-type equations. The Tau method, a spectral technique, is particularly effective in delivering highly accurate approximations across a broad range of differential problems. Its versatility in handling both initial-value and boundary-value problems makes it especially suitable for the classes of equations addressed in this work. This methodology has been integrated into <Emphasis FontCategory="NonProportional">Tau Toolbox</Emphasis>, a specialized software package developed for solving differential equations using the Lanczos Tau method. By leveraging the capabilities of <Emphasis FontCategory="NonProportional">Tau Toolbox</Emphasis>, we obtain efficient and reliable solutions that compare favourably with existing methods in the literature, while also benefiting from an intuitive and user-friendly interface.</p>

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An operational spectral Tau method for approximating solutions to functional differential equations

  • José M. A. Matos,
  • Paulo B. Vasconcelos,
  • José A. O. Matos

摘要

In this study, we present a detailed operational implementation of the Tau method for approximating solutions to functional differential equations, including but not limited to delay differential equations and pantograph-type equations. The Tau method, a spectral technique, is particularly effective in delivering highly accurate approximations across a broad range of differential problems. Its versatility in handling both initial-value and boundary-value problems makes it especially suitable for the classes of equations addressed in this work. This methodology has been integrated into Tau Toolbox, a specialized software package developed for solving differential equations using the Lanczos Tau method. By leveraging the capabilities of Tau Toolbox, we obtain efficient and reliable solutions that compare favourably with existing methods in the literature, while also benefiting from an intuitive and user-friendly interface.