Uniform error estimates of operational quadrature methods for nonlinear convolution equations on the half-line

Eggermont, P. P. B.; Lubich, Ch.

doi:10.1090/S0025-5718-1991-1052091-8

Uniform error estimates of operational quadrature methods for nonlinear convolution equations on the half-line
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by P. P. B. Eggermont and Ch. Lubich PDF

Math. Comp. 56 (1991), 149-176 Request permission

Abstract:

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 ${L^2}$ 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 ${L^p}$ spaces $(1 \leq p \leq \infty )$.

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On the input-output stability of nonlinear time-varying feedback systems. I and II

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