Superconvergence of the iterated degenerate kernel method

Superconvergence of the Iterated Degenerate Kernel Method

Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...

A Modified Degenerate Kernel Method for the System of Fredholm Integral Equations of the Second Kind

In this paper, the system of Fredholm integral equations of the second kind is investigated by using a modified degenerate kernel  method (MDKM). To construct a MDKM the source function is approximated by the same way of producing degenerate kernel. The interpolation is used to make the needed approximations. Lagrange polynomials are adopted for the interpolation. The equivalency of  proposed m...

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 ...

Singularity Analysis Via the Iterated Kernel Method

We provide exact and asymptotic counting formulas for five singular lattice path models in the quarter plane. Furthermore, we prove that these models have a non D-finite generating function. Résumé Nous présentons des résultats énumératives pour les cinq modèles de marches dans le quart de plan dites “singulière”. Nous prouvons que ces modéles sont non-holonome.