Numerical solutions for second-kind Volterra integral equations by Galerkin methods.

DOI10.1023/A:1022284616125zbMath1058.65148OpenAlexW1542241324MaRDI QIDQ1582521

Shuhua Zhang, Ming Rao, Yan Ping Lin

Publication date: 15 October 2000

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/33047

zbMATH Keywords

Volterra integral equationsa posteriori error estimatorsGalerkin methodsinterpolation post-processingiterative correctionconvergence and superconvergence

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Theoretical approximation of solutions to integral equations (45L05)

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Error analysis of Jacobi–Galerkin method for solving weakly singular Volterra–Hammerstein integral equations ⋮ Quasi-wavelet based numerical method for fourth-order partial integro-differential equations with a weakly singular kernel ⋮ The approximate solution of nonlinear Volterra integral equations of the second kind using radial basis functions ⋮ Approximate solution of the system of linear Volterra-Stieltjes integral equations of the second kind ⋮ Finite central difference/finite element approximations for parabolic integro-differential equations ⋮ Unnamed Item ⋮ Approximated superconvergent methods for Volterra Hammerstein integral equations ⋮ Local radial basis function scheme for solving a class of fractional integro‐differential equations based on the use of mixed integral equations ⋮ On a mixed Galerkin method for semi-explicit index-1 integro-differential algebraic equations ⋮ On the convergence of discontinuous Galerkin methods for integral-algebraic equations of index 1 ⋮ The Coiflet-Galerkin method for linear Volterra integral equations ⋮ Solving Volterra integral equations of the second kind by wavelet-Galerkin scheme ⋮ An \textit{hp}-version of the discontinuous Galerkin time-stepping method for Volterra integral equations with weakly singular kernels ⋮ Sawi decomposition method for Volterra integral equation with application ⋮ An efficient numerical algorithm to solve Volterra integral equation of second kind ⋮ Superconvergence of interpolated collocation solutions for weakly singular Volterra integral equations of the second kind ⋮ Approximate solution of Volterra-Stieltjes linear integral equations of the second kind with the generalized trapezoid rule ⋮ Superconvergence results of Legendre spectral projection methods for Volterra integral equations of second kind ⋮ A meshless local discrete Galerkin (MLDG) scheme for numerically solving two-dimensional nonlinear Volterra integral equations ⋮ Superconvergence of interpolated collocation solutions for Hammerstein equations ⋮ Meshless techniques for convection dominated problems ⋮ Superconvergence results for linear second-kind Volterra integral equations ⋮ Superconvergence results of iterated projection methods for linear Volterra integral equations of second kind ⋮ Approximation methods for second kind weakly singular Volterra integral equations ⋮ A Hermite collocation method for approximating a class of highly oscillatory integral equations using new Gaussian radial basis functions ⋮ Error analysis of Jacobi spectral Galerkin and multi-Galerkin methods for weakly singular Volterra integral equations ⋮ Legendre spectral Galerkin method for second-kind Volterra integral equations ⋮ A meshless local Galerkin method for solving Volterra integral equations deduced from nonlinear fractional differential equations using the moving least squares technique ⋮ On Discontinuous and Continuous Approximations to Second-Kind Volterra Integral Equations ⋮ A MESHLESS LOCAL GALERKIN INTEGRAL EQUATION METHOD FOR SOLVING A TYPE OF DARBOUX PROBLEMS BASED ON RADIAL BASIS FUNCTIONS ⋮ Quasi-wavelet method for time-dependent fractional partial differential equation

Cites Work

• A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations
• An immediate analysis for global superconvergence for integrodifferential equations
• An acceleration method for integral equations by using interpolation post-processing
• Higher accuracy methods for second-kind Volterra integral equations based on asymptotic expansions of iterated Galerkin methods
• The iterative correction method for Volterra integral equations
• On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations
• Extrapolation of the Iterated–Collocation Method for Integral Equations of the Second Kind
• Iterated Collocation Methods and Their Discretizations for Volterra Integral Equations
• The discrete collocation method for nonlinear integral equations
• The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
• Stieltjes Derivatives and $\beta $-Polynomial Spline Collocation for Volterra Integrodifferential Equations with Singularities
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