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 ź -smoothing property of a Volterra integral operator and some projectors. The L 2 - 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.

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