A numerical approach to the solution of Abel integral equations of the second kind with nonsmooth solution

DOI10.1016/0377-0427(90)90011-NzbMath0699.65088OpenAlexW2067009585MaRDI QIDQ913472

J. Abdalkhani

Publication date: 1990

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(90)90011-n

zbMATH Keywords

equationAbel integral equationsnonsmooth solutionweakly singular integral equationnonlinear integral

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Singular nonlinear integral equations (45G05)

Related Items

Optimal homotopy asymptotic and multistage optimal homotopy asymptotic methods for Abel Volterra integral equation of the second kind ⋮ A new approach to the numerical solution of weakly singular Volterra integral equations. ⋮ Product integration for Volterra integral equations of the second kind with weakly singular kernels ⋮ A new recursive formulation of the Tau method for solving linear Abel-Volterra integral equations and its application to fractional differential equations ⋮ The Puiseux expansion and numerical integration to nonlinear weakly singular Volterra integral equations of the second kind ⋮ An operational Haar wavelet method for solving fractional Volterra integral equations ⋮ A BLOCK BY BLOCK METHOD FOR SOLVING SYSTEM OF VOLTERRA INTEGRAL EQUATIONS WITH CONTINUOUS AND ABEL KERNELS ⋮ A rational basis for second-kind Abel integral equations ⋮ Hybrid Operators for Approximating Nonsmooth Functions and Applications on Volterra Integral Equations with Weakly Singular Kernels

Uses Software

• Algorithm 627

Cites Work

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• A smoothed projection method for singular, nonlinear Volterra equations
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• Iterated Collocation Methods and Their Discretizations for Volterra Integral Equations
• Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
• Weakly Singular Discrete Gronwall Inequalities
• Runge-Kutta Theory for Volterra Integral Equations of the Second Kind
• Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution
• High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels
• On Numerically Solving Nonlinear Volterra Integral Equations with Fewer Computations