The finite-section approximation for integral equations on the half-line
نویسندگان
چکیده
منابع مشابه
Integral Equations on the Half-Line: A Modified Finite-Section Approximation
We consider the approximate solution of integral equations of the form y(t) /if k(t,s)y(s)ds = f(t), where the conditions on k(t,s) are such that kernels of the Wiener-Hopf form k(t, s) = n(t s) are included in the analysis. The finite-section approximation, in which the infinite integral is replaced by }§ for some ß > 0, yields an approximate solution _Vß(t) that is known, under very general c...
متن کاملOn Asymptotic Behavior at Infinity and the Finite Section Method for Integral Equations on the Half-line
We consider integral equations on the halfline of the form x(s) − ∫∞ 0 k(s, t)x(t) dt = y(s) and the finite section approximation xβ to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e., xβ exists and is uniformly bounded in the space of bounded con...
متن کاملDegenerate 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...
متن کاملHomotopy approximation technique for solving nonlinear Volterra-Fredholm integral equations of the first kind
In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy...
متن کاملA finite difference method for the smooth solution of linear Volterra integral equations
The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
سال: 1987
ISSN: 0334-2700,1839-4078
DOI: 10.1017/s0334270000005506