Abel's integral operator: sparse representation based on multiwavelets
type: Item
instance of: scholarly article
title: Abel's integral operator: sparse representation based on multiwavelets
zbMATH Open document ID: 1466.45011
author: Behzad Nemati Saray
published in: BIT
publication date: 2021-05-19T00:00:00Z
review text: The author studies second kind Abel's integral equations through a multiwavelets Galerkin method. The corresponding Abel integral operator is represented upon a sparse matrix, and convergence analysis and numerical simulations are performed. The numerical calculations are deeply simplified by the fact that the decay property of the wavelet coefficients allows the reduction of the number of coefficients in the system of algebraic equations (obtained by the multiwavelets Galerkin method).
reviewed by: L. P. Castro
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 7349683
zbMATH Keywords: Abel integral equation
zbMATH Keywords: multiwavelets
zbMATH Keywords: Galerkin method
MaRDI profile type: Publication
full work available at URL: s10543-020-00832-1
OpenAlex ID: W3125356203
cites work: A Class of Bases in $L^2$ for the Sparse Representation of Integral Operators
cites work: Wavelet-Like Bases for the Fast Solution of Second-Kind Integral Equations
cites work: Adaptive solution of partial differential equations in multiwavelet bases
cites work: An Existence Theorem for Abel Integral Equations
cites work: Q3164471
cites work: Stability of collocation for weakly singular Volterra equations
cites work: Q3886814
cites work: Nonpolynomial Spline Collocation for Volterra Equations with Weakly Singular Kernels
cites work: The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes
cites work: A family of methods for Abel integral equations of the second kind
cites work: Product integration methods for second-kind Abel integral equations
cites work: The Analysis of Product Integration Methods for Abel's Equation using Discrete Fractional Differentiation
cites work: Numerical Methods in Scientific Computing, Volume I
cites work: Abel integral equations. Analysis and applications
cites work: Q4188970
cites work: Fast numerical solution of weakly singular Volterra integral equations
cites work: Adaptive multiresolution discontinuous Galerkin schemes for conservation laws
cites work: Propagation of simple non-linear waves in gas filled tubes with friction
cites work: Q5699297
cites work: The Convergence of Collocation Solutions in Continuous Piecewise Polynomial Spaces for Weakly Singular Volterra Integral Equations
cites work: A Stability Analysis of Convolution Quadraturea for Abel-Volterra Integral Equations
cites work: Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the First Kind
cites work: Runge-Kutta Theory for Volterra and Abel Integral Equations of the Second Kind
cites work: Q4488070
cites work: Heat transfer between solids and gases under nonlinear boundary conditions
cites work: Q3135829
cites work: Introduction to fractional differential equations
cites work: Solution of nonlinear Volterra integral equations with weakly singular kernel by using the HOBW method
cites work: Numerical approach based on fractional-order Lagrange polynomials for solving a class of fractional differential equations
cites work: An efficient algorithm for solving Volterra integro-differential equations based on Alpert's multi-wavelets Galerkin method
cites work: Sparse representation of system of Fredholm integro-differential equations by using alpert multiwavelets
cites work: Abel's Integral Equation as a Convolution Transform
cites work: Q5200269
DOI: 10.1007/S10543-020-00832-1
description: scientific article; zbMATH DE number 7349683