Legendre spectral projection methods for linear second kind Volterra integral equations with weakly singular kernels
نویسندگان
1 Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, India
2 Department of Mathematics \& Statistics, Indian Institute of Technology Kanpur, Kanpur 208 016, India
3 Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, India
doi
10.22075/ijnaa.2020.20716.2195چکیده
In this paper, Galerkin and iterated Galerkin methods are applied to approximate the linear second kind Volterra integral equations with weakly singular algebraic kernels using Legendre polynomial basis functions. We discuss the convergence results in both $L^{2}$ and infinity norms in two cases: when the exact solution is sufficiently smooth and non-smooth. We also apply Legendre multi-Galerkin and iterated Legendre multi-Galerkin methods and derive the superconvergence rates. Numerical results are given to verify the theoretical results.
