The regularization method for Fredholm integral equations of the first kind

B-spline Method for Solving Fredholm Integral Equations of the First ‎Kind

‎‎‎In this paper‎, we use the collocation method for to find an approximate solution of the problem by cubic B-spline basis.‎ The proposed method as a basic function led matrix systems, including band matrices and smoothness and capability to handle low calculative costly. ‎The absolute errors in the solution are compared to existing methods to verify the accuracy and convergent nature of propo...

The Regularization-Homotopy Method for the Two-Dimensional Fredholm Integral Equations of the First Kind

In this work, we consider two-dimensional linear and nonlinear Fredholm integral equations of the first kind. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method is used to find a solution to the equation. The application of this method is based upon converting the first kind of equation to the second kind by applying...

The regularization method for Fredholm integral equations of the first kind

A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind

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The modified degenerate kernel method for the multi-dimensional Fredholm integral equations of the second kind

In this paper, to investigate the multi-dimensional Fredholm integral equations of the second kind a modified degenerate kernel method is used. To construct the mentioned modified,  the source function is approximated by the same method which  employed to obtain a degenerate approximation of the kernel.  The Lagrange interpolation method is used to make the needed approximations. The error and ...