The operational matrix of Chebyshev polynomials for solving pantograph-type Volterra integro-differential equations

In this work, the Chebyshev collocation scheme is extended for the Volterra integro-differential equations of pantograph type. First, we construct the operational matrices of pantograph and derivative based on Chebyshev polynomials. Also, the obtained operational matrices are utilized to approximate the derivatives of unknown functions. Furthermore, a detailed analysis of convergence is discussed in the weighted square norm. We conduct some numerical experiments to verify the high performance of the suggested numerical approach. The results show that the computational scheme is accurate.