Superconvergence results of Legendre spectral projection methods for Volterra integral equations of second kind

DOI10.1007/s40314-017-0563-5zbMath1400.65064OpenAlexW2781413361MaRDI QIDQ1993403

Gnaneshwar Nelakanti, Moumita Mandal

Publication date: 5 November 2018

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-017-0563-5

zbMATH Keywords

projection methodsLegendre polynomialVolterra integral equationssmooth kernelssuperconvergence rates

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Volterra integral equations (45D05)

Related Items (13)

Discrete Legendre spectral methods for Hammerstein type weakly singular nonlinear Fredholm integral equations ⋮ Convergence analysis of Galerkin and multi-Galerkin methods for nonlinear-Hammerstein integral equations on the half-line using Laguerre polynomials ⋮ A collocation method based on roots of Chebyshev polynomial for solving Volterra integral equations of the second kind ⋮ A computational approach for solving third kind VIEs by collocation method based on radial basis functions ⋮ On the numerical solution of Volterra integral equations on equispaced nodes ⋮ Solving linear Volterra integral equations with a piecewise linear maximum entropy method ⋮ Approximation methods for system of linear Fredholm integral equations of second kind ⋮ Super-convergence analysis of collocation methods for linear and nonlinear third-kind Volterra integral equations with non-compact operators ⋮ Approximation methods for system of nonlinear Fredholm-Hammerstein integral equations ⋮ Convergence analysis of Galerkin and multi-Galerkin methods on unbounded interval using Hermite polynomials ⋮ Weakly singular linear Volterra integral equations: a Nyström method in weighted spaces of continuous functions ⋮ Superconvergence of system of Volterra integral equations by spectral approximation method ⋮ Projection methods for approximate solution of a class of nonlinear Fredholm integro-differential equations

Cites Work

• Convergence analysis of spectral Galerkin methods for Volterra type integral equations
• Legendre spectral Galerkin method for second-kind Volterra integral equations
• Discrete polynomial-based Galerkin methods for Fredholm integral equations
• Numerical solutions for second-kind Volterra integral equations by Galerkin methods.
• The iterative correction method for Volterra integral equations
• On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations
• Iteration methods for Fredholm integral equations of the second kind
• The discrete multi-projection method for Fredholm integral equations of the second kind
• Iterated Collocation Methods and Their Discretizations for Volterra Integral Equations
• Improvement by Iteration for Compact Operator Equations
• The Numerical Solution of Integral Equations of the Second Kind
• A superconvergence result for solutions of compact operator equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Spectral Methods
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