The Convergence of Collocation Solutions in Continuous Piecewise Polynomial Spaces for Weakly Singular Volterra Integral Equations

DOI10.1137/19M1245062zbMath1420.65139OpenAlexW2966373122MaRDI QIDQ5232310

Hui Liang, Hermann Brunner

Publication date: 2 September 2019

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1245062

zbMATH Keywords

uniform convergenceVolterra integral equationsweakly singular kernelscollocation solutionsglobally continuous piecewise polynomials

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

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Cites Work

• On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations
• On the divergence of collocation solutions in smooth piecewise polynomial spaces for Volterra integral equations
• The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes
• The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
• Continuous collocation approximations to solutions of first kind Volterra equations
• A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels
• Collocation Methods for Volterra Integral and Related Functional Differential Equations