Degenerate kernel schemes by wavelets for nonlinear integral equations on the real line

A degenerate kernel scheme is developed for nonlinear integral equations on the real line by approximation of kernels by wavelets. The rate of convergence of the approximate solutions is established in terms of the decay rate of the kernels andthe numbers of dilations and shifts used in approximation of the kernels. For linear equations, the Haar wavelet approximation is used and a numerical example is included.