An adaptive Huber method with local error control, for the numerical solution of the first kind Abel integral equations

DOI10.1007/s00607-008-0010-yzbMath1155.65398OpenAlexW2050795087MaRDI QIDQ956692

Lesław K. Bieniasz

Publication date: 25 November 2008

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-008-0010-y

zbMATH Keywords

adaptive methodsa posteriori error estimationproduct-integrationcomputational electrochemistryHuber methodthe first kind Abel 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)

Related Items (9)

Initialisation of the adaptive Huber method for solving the first kind Abel integral equation ⋮ An adaptive Huber method for nonlinear systems of Volterra integral equations with weakly singular kernels and solutions ⋮ A fully discrete Galerkin method for Abel-type integral equations ⋮ An adaptive Huber method for weakly singular second kind Volterra integral equations with non-linear dependencies between unknowns and their integrals ⋮ An adaptive Huber method for non-linear systems of weakly singular second kind Volterra integral equations ⋮ Approximate solution of some nonlinear classes of Abel integral equations using hybrid expansion ⋮ Numerical solution of nonlinear weakly singular Volterra integral equations of the first kind: an \textit{hp}-version collocation approach ⋮ Automatic simulation of electrochemical transients by the adaptive Huber method for Volterra integral equations involving kernel terms \(\exp[ -\alpha (t - \tau )\text{erex} \{[\beta (t - \tau )]^{1/2}\}\) and \(\exp[ - \alpha (t - \tau )]\text{daw} \{[\beta (t - \tau )]^{1/2}\}\)] ⋮ Adaptive Huber scheme for weakly singular fractional integro-differential equations

Uses Software

• ELSIM

Cites Work

• Adaptive collocation methods for Volterra integral and integro-differential equations
• Abel integral equations. Analysis and applications
• An estimate for the Hausdorff dimension of attractor for two-dimensional equations of Oldroyd fluids
• Adaptive discretization of an integro-differential equation with a weakly singular convolution kernel.
• Convolution quadrature revisited
• A product integration method for a class of singular first kind Volterra equations
• Adaptive, Fast, and Oblivious Convolution in Evolution Equations with Memory
• High-accuracy product integration methods for the Abel equation, and their application to a problem in scattering theory
• The Analysis of Product Integration Methods for Abel's Equation using Discrete Fractional Differentiation
• Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
• Rational Chebyshev Approximations for the Error Function
• Chebyshev Approximations for Dawson's Integral
• Product Integration for the Generalized Abel Equation
• Eine Näherungsmethode zur Auflösung Volterrascher Integralgleichungen
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: An adaptive Huber method with local error control, for the numerical solution of the first kind Abel integral equations