Fredholm equations for non-symmetric kernels with applications to iterated integral operators
نویسندگان
چکیده
We give the Jordan form and the Singular Value Decomposition for an integral operator N with a non-symmetric kernel N(y, z). This is used to give solutions of Fredholm equations for non-symmetric kernels, and to determine the behaviour of N n and (NN ∗)n for large n.
منابع مشابه
COLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS
In this paper it is shown that the use of uniform meshes leads to optimal convergence rates provided that the analytical solutions of a particular class of Fredholm-Volterra integral equations (FVIEs) are smooth.
متن کاملSuperconvergence of the Iterated Galerkin Methods for Hammerstein Equations
In this paper, the well known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numeric...
متن کاملThe approximate solutions of Fredholm integral equations on Cantor sets within local fractional operators
In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools ...
متن کاملApplying fuzzy wavelet like operator to the numerical solution of linear fuzzy Fredholm integral equations and error analysis
In this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy Fredholm integral equations of the second kind with arbitrary kernels. We give the convergence conditions and an error estimate. Also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....
متن کاملHilbert Space Analysis of Integral Equations
This paper examines the theory of solving certain classes of integral equations using functional analysis methods of Hilbert Space. Included are equations with symmetric kernels and their associated self-adjoint linear operators, and in particular the Fredholm equation. The Hilbert Space methods, while taking time and effort to establish, prove rewarding in that they then simplify approaches to...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 204 شماره
صفحات -
تاریخ انتشار 2008