Numerical Analysis Of The Index 1 Integral Algebraic Equation Based On The Block Pulse Function

This paper mainly focuses on solving index-1 integral algebraic equations numerically based on block pulse function.Generally,integral algebraic equations are coupled systems of the first-kind and second-kind Volterra integral equations,whose models exist widely in physics,chemistry,engineering and many other fields of science and technology.In this paper,we use the block pulse function to solve index-1 integral algebraic equation indirectly and directly,respectively.For the indirect method,the index-1integral algebraic equation is first transformed into a system of Volterra integral equations,then impulse functions is used to approximate the obtained system.The existence and uniqueness of the corresponding numerical solution are proved,and the convergence is analyzed in detail.In order to solve the index-1 integral algebraic equation by the direct method,first,as for the first-kind Volterra integral equation,we give the numerical scheme of the block-pulse function,and prove the existence and uniqueness of the numerical solution and the 1-order convergence.Then,based on the numerical analysis of the first-kind Volterra integral equation,we study the index-1 integral algebraic equation: the numerical scheme of the block-pulse function is given;the existence and uniqueness of the numerical solution are proved;and the1-order convergence order is derived.Finally,some numerical examples are given to verify our theoretical results.