Abstract :
In this paper we are concerned with the numerical analysis of the collocation method based on
graded meshes of second kind integral equations on the real line of the form
φ(s) = ψ(s)+ R
κ(s − t)z(t)φ(t)dt, s ∈ R,
where κ ∈ L1(R), z ∈ L∞(R), and ψ ∈ BC(R), the space of bounded continuous complex-valued
functions on R, are assumed known and the function φ ∈ BC(R) is to be determined. We introduce
some new graded meshes for the collocation method of the integral equation, which are different from
those used previously for the Wiener–Hopf integral equation in the case when the solution decays
exponentially at infinity, and establish optimal local and global L∞-norm error estimates under the
condition that the solution decays only polynomially at infinity.
2004 Elsevier Inc. All rights reserved.
