Operational Tau method for singular system of Volterra integro-differential equations

The Legendre spectral Tau matrix formulation is proposed to approximate solution of singular system of Volterra integro-differential equations. The existence and uniqueness solution of this system are investigated by means of the υυ-smoothing property of a Volterra integral operator and some projectors. The L2−L2−convergence of the numerical method is analyzed. It is proved theoretically and demonstrated numerically that the proposed method converges exponentially. Finally, two numerical examples illustrate the theoretical results.