摘要：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. MSC:65R20.
关键词：integral algebraic equations ; Jacobi collocation method ; system of weakly singular Volterra equations ; index of IAEs ; error analysis
