AbstractWe consider the approximate solution of Wiener‐Hopf integral equations by Galerkin, collocation and Nyström methods based on piecewise polynomials where accuracy is achieved by increasing simultaneously the number of mesh points and the degree of the polynomials. We look for the stability of those methods in theLqnorm, 1≤q≤∞. Provided the exact solution is analytic on the half‐axis and decays exponentially at infinity, we prove an exponential rate of convergence with respect to the number of degrees