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Mathematics of Computation

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


Authors: P. P. B. Eggermont and Ch. Lubich
Journal: Math. Comp. 56 (1991), 149-176
MSC: Primary 65R20; Secondary 45D05, 47H15, 47H17
MathSciNet review: 1052091
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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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DOI: http://dx.doi.org/10.1090/S0025-5718-1991-1052091-8
Article copyright: © Copyright 1991 American Mathematical Society