Efficient Taylor-based solver for proportional-delay Volterra equations

Abstract

This study introduces a Taylor Collocation Method for Volterra integral equations with proportional delay. The proposed method employs Taylor polynomials to approximate the solution through collocation at selected nodes, achieving high-order accuracy for smooth problems. A rigorous convergence analysis establishes the theoretical foundation of the method. Numerical experiments evaluate performance against existing schemes, validating the Taylor Collocation Method as an efficient and accurate technique for solving proportional-delay integral equations.