Research On The Configuration Method Of A Class Of Index 2 Delayed Integral Algebraic Equations

In this article,we mainly focus on collocation methods for a class of semi-explicit index-2 integral-algebraic equations with delay.Integral-algebraic equations are coupled systems of the first and second Volterra integral equations,and this kind of equations is also an important branch of integral equations.First,the current research status of Volterra integral equations and integral-algebraic equations is reviewed.Next,for a class of semi-explicit index-2 integral-algebraic equations with delay,resorting to the resolvent representation of the an-alytic solution and the induction argument,the existence and uniqueness of the analytic solution are proved interval by interval according to the delay.Then the regularity is described in detail,which shows how does the delay affect the regularity of the solution for this kind of equations.Last,collocation methods are employed to solve the index-2 integral-algebraic equations with delay.The corresponding collo-cation scheme is given,and the convergence of the numerical method is investigated thoroughly.