Spline Collocation for Cordial Volterra Integral Equations

DOI10.1080/01630561003757710zbMath1195.65230OpenAlexW1998885375MaRDI QIDQ3578015

Gennadi Vainikko

Publication date: 13 July 2010

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630561003757710

zbMATH Keywords

spline collocationcordial Volterra operatorsinterpolation operatornoncompact operatorslinear Volterra integral equations of the second kindLagrange fundamental polynomials

Mathematics Subject Classification ID

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

Related Items

First Kind Cordial Volterra Integral Equations 1 ⋮ First Kind Cordial Volterra Integral Equations 2 ⋮ A priori mesh grading in collocation solution of noncompact Volterra integral equations with diagonal singularity ⋮ Fractional collocation method for third-kind Volterra integral equations with nonsmooth solutions ⋮ On a class of noncompact weakly singular Volterra integral equations: theory and application to fractional differential equations with variable coefficient ⋮ Smoothing transformation and collocation methods for third-kind linear Volterra integral equations ⋮ Modified Euler's method with a graded mesh for a class of Volterra integral equations with weakly singular kernel ⋮ Composite quadrature rules for a class of weakly singular Volterra integral equations with noncompact kernels ⋮ Analysis of collocation methods for nonlinear Volterra integral equations of the third kind ⋮ Spectral Collocation Method for a Class of Integro-Differential Equations with Erdelyi-Kober Fractional Operator ⋮ Analysis of blow-up behavior of solutions to CVIEs ⋮ Collocation methods for cordial Volterra integro-differential equations ⋮ Spline Collocation-Interpolation Method for Linear and Nonlinear Cordial Volterra Integral Equations ⋮ Legendre-Galerkin methods for third kind VIEs and CVIEs ⋮ Cordial Volterra integral operators in spaces \(L^p(0,T)\)

Cites Work

• Integral equations with diagonal and boundary singularities of the kernel
• Superconvergence of collocation methods for a class of weakly singular Volterra integral equations
• Convergence of spline collocation for Volterra integral equations
• Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations
• High-order methods for the numerical solution of Volterra integro- differential equations
• Smoothing transformation and piecewise polynomial collocation for weakly singular Volterra integral equations
• Numerical methods for integral equations of Mellin type
• A Spline Product Quasi-interpolation Method for Weakly Singular Fredholm Integral Equations
• Cordial Volterra Integral Equations 1
• On Spline Approximation for a Class of Non‐Compact Integral Equations
• Cordial Volterra Integral Equations 2
• The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Error estimates and extrapolation for the numerical solution of Mellin convolution equations

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