Galerkin and multi-Galerkin methods for weakly singular Volterra-Hammerstein integral equations and their convergence analysis

DOI10.1007/s40314-020-1100-5zbMath1449.65362OpenAlexW3006667252MaRDI QIDQ2176202

Kapil Kant, Gnaneshwar Nelakanti

Publication date: 4 May 2020

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

Full work available at URL: https://doi.org/10.1007/s40314-020-1100-5

zbMATH Keywords

Galerkin methodVolterra integral equationsweakly singular kernelspiecewise polynomialssuperconvergence ratesmulti-Galerkin method

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Volterra integral equations (45D05) Theoretical approximation of solutions to integral equations (45L05)

Related Items (8)

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 ⋮ NEW SOLITARY WAVE SOLUTIONS FOR THE FRACTIONAL JAULENT–MIODEK HIERARCHY MODEL ⋮ Convergence analysis of a novel fractional product integration method for solving the second kind weakly singular Volterra integral equations with non-smooth solutions based on Jacobi polynomials ⋮ Approximated superconvergent methods for Volterra Hammerstein integral equations ⋮ A novel method for linear and nonlinear fractional Volterra integral equations via cubic hat functions ⋮ Jacobi Spectral Galerkin Methods for a Class of Nonlinear Weakly Singular Volterra Integral Equations ⋮ Approximation methods for system of nonlinear Fredholm-Hammerstein integral equations

Cites Work

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• A Nyström interpolant for some weakly singular nonlinear Volterra integral equations
• Polynomially based multi-projection methods for Fredholm integral equations of the second kind
• Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind
• A hybrid collocation method for a nonlinear Volterra integral equation with weakly singular kernel
• A nonlinear integral equation associated with gas absorption in a liquid
• Superconvergence results of Legendre spectral projection methods for weakly singular Fredholm-Hammerstein integral equations
• Legendre spectral projection methods for Fredholm-Hammerstein integral equations
• Convergence Analysis of Legendre Spectral Galerkin Method for Volterra-Fredholm-Hammerstein Integral Equations
• Volterra Integral Equations
• An $hp$-version Legendre-Jacobi spectral collocation method for Volterra integro-differential equations with smooth and weakly singular kernels
• Nonpolynomial Spline Collocation for Volterra Equations with Weakly Singular Kernels
• Runge-Kutta Theory for Volterra and Abel Integral Equations of the Second Kind
• An $h$-$p$ Version of the Continuous Petrov--Galerkin Finite Element Method for Volterra Integro-Differential Equations with Smooth and Nonsmooth Kernels
• The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes
• Galerkin Methods for Second Kind Integral Equations with Singularities
• Diffusion in a Semi-Infinite Region with Nonlinear Surface Dissipation
• The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
• A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels
• Product integration for Volterra integral equations of the second kind with weakly singular kernels
• Superconvergence Results for Weakly Singular Fredholm–Hammerstein Integral Equations
• Smoothness of Solutions of Volterra Integral Equations with Weakly Singular Kernels
• Heat transfer between solids and gases under nonlinear boundary conditions

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