Fifth-Kind Chebyshev Spectral Collocation Treatment for the Volterra Integro-Differential Equation of the Third Kind

In this research work, we offer an efficient spectral numerical scheme for handling the Volterra integro-differential of the third kind via Chebyshev polynomials of the fifth kind. The celebrated fundamentals and relations were stated with some details. With the aid of the spectral collocation method and the properties of Chebyshev polynomials, the singular Volterra integro-differential equation with its initial condition was transformed into a system of algebraic equations. The convergence and error analyses were discussed in depth. The validity and applicability of the method were tested and verified through three numerical examples, with the absolute errors reported in tables an graphs.