Analysis of Collocation Methods for Generalized Auto-Convolution Volterra Integral Equations

DOI10.1137/15M1019362zbMath1416.65560MaRDI QIDQ2798203

Hermann Brunner, Ran Zhang, Hui Liang

Publication date: 4 April 2016

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

zbMATH Keywords

collocation methodssuperconvergenceoptimal order of convergenceexistence and regularity of solutionsauto-convolution Volterra integral equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Volterra integral equations (45D05)

Related Items (14)

Collocation boundary value methods for auto-convolution Volterra integral equations ⋮ Exponential fitting collocation methods for a class of Volterra integral equations ⋮ Analysis of collocation methods for a class of third-kind auto-convolution Volterra integral equations ⋮ On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case ⋮ High-order convergence of multistep collocation methods for nonstandard Volterra integral equations ⋮ Optimal error estimates for Chebyshev approximations of functions with endpoint singularities in fractional spaces ⋮ A linearized fourth-order compact ADI method for phytoplankton-zooplankton model arising in marine ecosystem ⋮ Continuous piecewise polynomial collocation methods for generalized auto-convolution Volterra integral equations ⋮ Numerical Analysis and Computational Solution of Integro-Differential Equations ⋮ Unnamed Item ⋮ The linear barycentric rational quadrature method for auto-convolution Volterra integral equations ⋮ Highly stable multistep Runge-Kutta methods for Volterra integral equations ⋮ Barycentric rational collocation methods for Volterra integral equations with weakly singular kernels ⋮ Theoretical and numerical analysis of third-kind auto-convolution Volterra integral equations

Cites Work

• Unnamed Item
• Unnamed Item
• Existence and uniqueness theorems for a nonlinear integral equation
• On a class of nonlinear convolution equations
• Positive solutions of a quadratic integral equation
• Autoconvolution equations and special functions II
• A nonlinear integral equation
• Analysis of collocation solutions for nonstandard Volterra integral equations
• Inverse problems of memory reconstruction
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Die Anwendung des Operatorenkalküls von Jan Mikusiński auf lineare Integralgleichungen vom Faltungstypus

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