Numerical solution of Abel's integral equation by using Legendre wavelets
From MaRDI portal
Publication:2369186
DOI10.1016/j.amc.2005.07.032zbMath1088.65124OpenAlexW2087293778MaRDI QIDQ2369186
Publication date: 28 April 2006
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2005.07.032
Numerical methods for integral equations (65R20) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)
Related Items (61)
Numerical solution of high-order linear Volterra integro-differential equations by using Taylor collocation method ⋮ A numerical method to solve a class of linear integro-differential equations with weakly singular kernel ⋮ An approximate method for Abel inversion using Chebyshev polynomials ⋮ Legendre-Galerkin method for the linear Fredholm integro-differential equations ⋮ Approximate solutions of the generalized Abel's integral equations using the extension Khan's homotopy analysis transformation method ⋮ The approximate solution of nonlinear Volterra integral equations of the second kind using radial basis functions ⋮ Hermite multiwavelets representation for the sparse solution of nonlinear Abel's integral equation ⋮ An interpolation-based method for solving Volterra integral equations ⋮ A Legendre reproducing kernel method with higher convergence order for a class of singular two-point boundary value problems ⋮ Meshless procedure for highly oscillatory kernel based one-dimensional Volterra integral equations ⋮ An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics ⋮ An efficient numerical method for solving Abel integral equation ⋮ Jacobi collocation approximation for solving multi-dimensional Volterra integral equations ⋮ Unnamed Item ⋮ Non-polynomial spline functions and Quasi-linearization to approximate nonlinear Volterra integral equation ⋮ Solving Volterra integral equations of the second kind by sigmoidal functions approximation ⋮ Finding optimal convergence control parameter in the homotopy analysis method to solve integral equations based on the stochastic arithmetic ⋮ Optimal formulas for the approximate-analytical solution of the general Abel integral equation in the Sobolev space ⋮ A projection method for Volterra integral equations in weighted spaces of continuous functions ⋮ A new operational method to solve Abel's and generalized Abel's integral equations ⋮ An efficient algorithm based on the pseudospectral method for solving Abel's integral equation using Hermite cubic spline scaling bases ⋮ Meshless methods for one-dimensional oscillatory Fredholm integral equations ⋮ A combination of the quasilinearization method and linear barycentric rational interpolation to solve nonlinear multi-dimensional Volterra integral equations ⋮ An effective procedure for solving Volterra integro-differential equations ⋮ An efficient technique for finding the eigenvalues and the eigenelements of fourth-order Sturm-Liouville problems ⋮ Application of the Fractional Differential Transform Method to the First Kind Abel Integral Equation ⋮ Numerical solution of Abel's integral equations using Hermite wavelet ⋮ The stability study of numerical solution of Fredholm integral equations of the first kind with emphasis on its application in boundary elements method ⋮ Unnamed Item ⋮ Legendre wavelet residual approach for moving boundary problem with variable thermal physical properties ⋮ Approximate solutions of a sum-type fractional integro-differential equation by using Chebyshev and Legendre polynomials ⋮ Bernoulli polynomials for the numerical solution of some classes of linear and nonlinear integral equations ⋮ Unnamed Item ⋮ Approximate solution of some nonlinear classes of Abel integral equations using hybrid expansion ⋮ An efficient numerical algorithm to solve Volterra integral equation of second kind ⋮ On Filon methods for a class of Volterra integral equations with highly oscillatory Bessel kernels ⋮ Legendre wavelet Galerkin method for solving ordinary differential equations with non-analytic solution ⋮ Application of orthonormal Bernoulli polynomials for approximate solution of some Volterra integral equations ⋮ Using of Bernstein spectral Galerkin method for solving of weakly singular Volterra-Fredholm integral equations ⋮ Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations ⋮ Unnamed Item ⋮ Bernstein series solution of a class of linear integro-differential equations with weakly singular kernel ⋮ Approximation of function belonging to generalized Hölder's class by first and second kind Chebyshev wavelets and their applications in the solutions of Abel's integral equations ⋮ A new approach to the numerical solution of Volterra integral equations by using Bernstein's approximation ⋮ A generalized barycentric rational interpolation method for generalized Abel integral equations ⋮ Operational matrix approach for solution of integro-differential equations arising in theory of anomalous relaxation processes in vicinity of singular point ⋮ Numerical schemes for the generalized Abel's integral equations ⋮ An efficient and stable Lagrangian matrix approach to Abel integral and integro-differential equations ⋮ The combined reproducing kernel method and Taylor series to solve nonlinear Abel’s integral equations with weakly singular kernel ⋮ Block-pulse functions approach to numerical solution of Abel’s integral equation ⋮ A numerical approach for solving nonlinear fractional Volterra–Fredholm integro-differential equations with mixed boundary conditions ⋮ Efficient algorithms to solve singular integral equations of Abel type ⋮ An operational Haar wavelet method for solving fractional Volterra integral equations ⋮ Approximate solutions of Volterra integral equations by an interpolation method based on ramp functions ⋮ B-polynomial multiwavelets approach for the solution of Abel's integral equation ⋮ Unnamed Item ⋮ Analytical solution of Abel integral equation arising in astrophysics via Laplace transform ⋮ Bernstein polynomials based iterative method for solving fractional integral equations ⋮ A numerical algorithm for a class of nonlinear fractional Volterra integral equations via modified hat functions ⋮ Hybrid Operators for Approximating Nonsmooth Functions and Applications on Volterra Integral Equations with Weakly Singular Kernels ⋮ Bernoulli polynomials collocation for weakly singular Volterra integro-differential equations of fractional order
Cites Work
- Implicitly linear collocation methods for nonlinear Volterra equations
- Asymptotic error expansion of a collocation-type method for Volterra- Hammerstein integral equations
- A new approach to the numerical solution of weakly singular Volterra integral equations.
- The Legendre wavelets operational matrix of integration
- Fast wavelet transforms and numerical algorithms I
- Wavelets
- The Haar wavelets operational matrix of integration
- Unnamed Item
- Unnamed Item
This page was built for publication: Numerical solution of Abel's integral equation by using Legendre wavelets