Direct Method Of Singular Integral Equation On Open Arc

In this paper,we considered the singular integral equation on L an open arc.The L is a cravk curve on the plane.Both coefficients and the kernel density are holomorphic functions.In the case of canonical,we considered the direct method of Cauchy type singular integral is not solved by the step of Fredholm equation or Riemann boundary value problem.We use Plemelj formula and generalized residue theorem to transform the integral equation into an algebraic equation.Then we give the solution directly.The first chapter introduces the background of singular integral equations and the development achievements at home and abroad.The second chapter introduces some related basic knowledge about the singular integral equation and the related theorem,definitions,and lemma,the basics are based on the singular integral equation in a closed smooth curve,the third chapter using the second knowledge and the basis of existing achievements,the direct solution openings arc singular integral,due to the openings on the arc of singular integral equation calculation more troublesome,so the corresponding conditions for direct solution of arc and shedding;The fourth chapter is the specific algorithm of the open arc from 0 to 1.