Error bound for integral equations on the half line

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...

System of singular second-order differential equations with integral condition on the positive half-line

In this work, we are concerned with the existence and the multiplicity of nontrivial positive solutions for a boundary value problem of a system of second-order differential equations subject to an integral boundary condition and posed on the positive half-line. The positive nonlinearities depend on the solution and their derivatives and may have space singularities. New existence results of si...

On 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...

Linear Systems and Half-Line Integral Representations

We give an expression for the most general input-output map associated with the members of a certain important large family of causal time-invariant linear systems. This expression is a uniform limit of a convolution. We also give a necessary and sufficient condition under which the limit can be written as a convolution, and we relate this to the concepts of an impulse response and a q-response...

Fuzzy Galerkin method for solving Fredholm integral equations with error analysis