Numerical solution and structural analysis of two-dimensional integral-algebraic equations

The υ-smoothing property of a one-dimensional Volterra integral operator and some projectors (Liang and Brumer, SIAM J. Numer. Anal. 51, 2238–2259 (2013)) are extended for two-dimensional integral-algebraic equations (TIAEs). Using these concepts, we decompose the given general TIAEs into mixed systems of two-dimensional Volterra integral equations (TVIEs) consisting of second- and first-kind TVIEs. Numerical technique based on the Chebyshev polynomial collocation methods is presented for the solution of the mixed TVIE system. Global convergence results are established and the performance of the numerical scheme is illustrated by means of some test problems.