ON THE EXPONENTIAL CONVERGENCE OF SPLINE APPROXIMATION METHODS FOR WIENER-HOPF EQUATIONS

We consider the approximate solution Of WIENER-HOPF integral equations by GALERKIN, collocation and NYSTROM methods based on piecewise polyn omials where accuracy is achieved by increasing simultaneously the num ber of mesh points and the degree of the polynomials. We look for the stability of those methods in the L(q) norm, 1 less-than-or-equal-to q less-than-or-equal-to infinity. Provided the exact solution is analyt ic on the half-axis and decays exponentially at infinity, we prove an exponential rate of convergence with respect to the number of degrees of freedom.