Representation of the exact solution and a stability analysis on the Fredholm integral equation of the first kind in reproducing kernel space

DOI10.1016/j.amc.2006.05.049zbMath1108.65126OpenAlexW1974455565MaRDI QIDQ858829

Ming-Gen Cui, Hong Du

Publication date: 11 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.05.049

zbMATH Keywords

ill-posed problem

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Fredholm integral equations (45B05)

Related Items (12)

Solving Fredholm integral equation of the first kind using Gaussian process regression ⋮ Projected Tikhonov regularization method for Fredholm integral equations of the first kind ⋮ The solution of Bessel function dual integral equations by converting to the first kind Fredholm Integral Equation: an extension of Noble’s solution ⋮ Eigenstates and scattering solutions for billiard problems: a boundary wall approach ⋮ Using reproducing kernel for solving a class of partial differential equation with variable-coefficients ⋮ Reproducing kernel method of solving singular integral equation with cosecant kernel ⋮ Reproducing kernel method for solving Fredholm integro-differential equations with weakly singularity ⋮ A splitting iterative method for solving second kind integral equations in reproducing kernel spaces ⋮ Stability and error analysis of the reproducing kernel Hilbert space method for the solution of weakly singular Volterra integral equation on graded mesh ⋮ Some error estimates for solving Volterra integral equations by using the reproducing kernel method ⋮ Error analysis of reproducing kernel Hilbert space method for solving functional integral equations ⋮ New algorithm for second-order boundary value problems of integro-differential equation

Uses Software

• NLREG
• GENEREG

Cites Work

• A stability estimate on the regularized solution of the backward heat equation.
• Central difference schemes in time and error estimate on a non-standard inverse heat conduction problem
• An introduction to the mathematical theory of inverse problems
• A generalized regularization method for nonlinear ill-posed problems enhanced for nonlinear regularization terms
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