Generalized quadrature for solving singular integral equations of Abel type in application to infrared tomography

DOI10.1016/j.apnum.2016.03.004zbMath1416.65552arXiv1509.02586OpenAlexW2964112625MaRDI QIDQ284930

Denis Nikolaevich Sidorov, Valery Sizikov

Publication date: 18 May 2016

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.02586

zbMATH Keywords

regularizationintegral equationsquadratureAbel equationsingular kernelsgeneralized quadratureinfrared tomography

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Biomedical imaging and signal processing (92C55) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Related Items (13)

Analytical discussion for the mixed integral equations ⋮ Polynomial spline collocation method for solving weakly regular Volterra integral equations of the first kind ⋮ Dynamical strategy on homotopy perturbation method for solving second kind integral equations using the CESTAC method ⋮ On a discussion of Volterra-Fredholm integral equation with discontinuous kernel ⋮ A novel numerical optimality technique to find the optimal results of Volterra integral equation of the second kind with discontinuous kernel ⋮ Singular expansions and collocation methods for generalized Abel integral equations ⋮ Bivariate barycentric rational interpolation method for two dimensional fractional Volterra integral equations ⋮ Numerical Analysis of Fractional Order Integral Dynamical Models with Piecewise Continuous Kernels ⋮ Application of reproducing kernel Hilbert space method for solving a class of nonlinear integral equations ⋮ A meshless local discrete Galerkin (MLDG) scheme for numerically solving two-dimensional nonlinear Volterra integral equations ⋮ Numerical schemes for the generalized Abel's integral equations ⋮ Control of accuracy on Taylor-collocation method for load leveling problem ⋮ An iterative multistep kernel based method for nonlinear Volterra integral and integro-differential equations of fractional order

Uses Software

• EDA

Cites Work

• Efficient algorithms to solve singular integral equations of Abel type
• Abel integral equations. Analysis and applications
• Solving Abel's type integral equation with Mikusinski's operator of fractional order
• Numerical solution of the singular Abel integral equation by the generalized quadrature method
• The numerical solution of Abel's integral equation
• Numerical Solution of Volterra Integral Equations of the First Kind with Piecewise Continuous Kernel
• Discrete Inverse Problems
• Exploratory Data Analysis with MATLAB
• Inversion of Abel’s Integral Equation by Means of Orthogonal Polynomials
• Approximate methods for singular integral equations in exceptional cases
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Generalized quadrature for solving singular integral equations of Abel type in application to infrared tomography