Retraction:Jacobi spectral solution for weakly singular integral algebraic equations of index-1

This paper is concerned with obtaining the approximate solution of a class of semi-explicit Integral Algebraic equations (IAEs) of index-1 with weakly singular kernels. Some function transformations and variable transformations are used to change the equations into integral equations defined on the standard interval [-1, 1], so that the solution of the new system possesses better regularity and the Jacobi orthogonal polynomial theory can be applied conveniently. A Jacobi collocation method is proposed and its convergence analysis is provided, which theoretically justifies the spectral rate of convergence. The numerical results are given to verify our theoretical analysis.