COLLOCATION METHODS FOR A CLASS OF INTEGRO-DIFFERENTIAL ALGEBRAIC EQUATIONS

A class of index-1 integro-differential algebraic equations modeling a hydraulic circuit that feed a combustion process is considered. The existence, uniqueness and regularity are analyzed in detail. Two kinds of collocation methods are employed to solve the equation numerically. For the first one, the derivative and algebraic components are approximated in globally continuous and discontinuous polynomial spaces, respectively; and for another one, both the derivative and algebraic components are solved in globally continuous piecewise polynomial spaces. The convergence, global and local surperconvergence are described for these two classes of collocation methods. Some numerical experiments are given to illustrate the obtained theoretical results.