Research On Multi-step Configuration Method Of Index 1 Integral Algebraic Equation

In this paper,we deal with the multistep collocation method to integral-algebraic equations of index 1.The specific models of integral-algebraic equations are widely used in many fields,such as physics,chemistry and engineering.So it has important theoretical and practical significance.In this paper,we first review the research status of the Volterra integral equa-tions and integral-algebraic equations.Then the multistep collocation scheme of the first-kind Volterra integral equations is given and the existence and uniqueness of the collocation solution are proved.In particular,for cm=1,the convergence of 2-steps and 3-steps collocation methods is given in detail.Next,we apply collocation method to integral-algebraic equations of index 1 in continuous piecewise polyno-mial spaces,which actually is the 2-steps collocation method for integral-algebraic equations of index 1.The existence and uniqueness of the collocation solutions in continuous polynomial space are given and the convergence is analyzed when cm=1.Last,on the basis of the above work,we study the multistep collocation method for integral-algebraic equations of index 1,and give the collocation scheme of the col-location method.Then the existence and uniqueness of the collocation method are also proved and the convergence of the multistep collocation method is analyzed.In addition,at the end of each chapter some numerical experiments are given to verify the theoretical analysis.