Legendre spectral projection methods for linear second kind Volterra integral equations with weakly singular kernels

	Legendre spectral projection methods for linear second kind Volterra integral equations with weakly singular kernels
International Journal of Nonlinear Analysis and Applications
مقاله 113، دوره 13، شماره 2، مهر 2022، صفحه 1377-1397 اصل مقاله (473.87 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.20716.2195
نویسندگان
Samiran Chakraborty¹؛ Kapil Kant^* ²؛ Gnaneshwar Nelakanti¹
¹Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, India
²Department of Mathematics \& Statistics, Indian Institute of Technology Kanpur, Kanpur 208 016, India
چکیده
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.
کلیدواژه‌ها
Volterra integral equations؛ Galerkin method؛ Multi-Galerkin method؛ Weakly singular kernels؛ Legendre polynomials
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