Mapped Spectral Collocation Methods For Volterra Integral Equations With Noncompact Kernels

This paper firstly is devoted to solve weakly singular Volterra integral equations with noncompact kernels and the Volterra delay integro-differential equations,which differ from the well-known case of Abel-type equations.We consider the mapped Laguerre spectral method to deal with the singularity,for the classic spectral algorithms are not suitable for this type of equation with logarithmic kernels.The construction and analysis of log orthogonal functions collocation method are presented in this paper and some numerical examples are included to show the efficiency of the proposed method.And we investigate the Fredholm integral equation with singular kernel.