Uniform Error Estimates of Operational Quadrature Methods for Nonlinear Convolution Equations on the Half-Line

We study uniform error estimates of operational quadrature methods for nonlinear convolution equations on the half-line. Equations of this kind arise in control engineering and diffusion problems. The essential ingredients are the stability of the operational quadrature method in an setting, which is inherited from the continuous equation by its very construction, and a theorem that says that the behavior of the linearized equations is the same in all spaces <!-- MATH $(1 \leq p \leq \infty )$ --> .