The time discretization in classes of integro‐differential equations with completely monotonic kernels: Weighted asymptotic convergence |
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| Authors: | Da Xu |
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| Affiliation: | Department of Mathematics, Hunan Normal University, Changsha, Hunan, People's Republic of China |
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| Abstract: | We consider the time discretization for the solution of the equation  with  . Here, the operators Lj are densely defined positive self‐adjoint linear operator on a Hilbert space H and have spectral decompositions with respect to a common resolution of the identity  in H . The kernel functions  , are assumed to be completely monotonic on (0,∞) and locally integrable, but not constant. The considered time discretization method comes from Da Xu, Science China Mathematics 56 (2013), 395–424], where the backward Euler method is combined with order one convolution quadrature for approximating the integral term. In this article, the convergence properties of the time discretization are given in the weighted  and  norm, where ρ is a given weighted function. Numerical experiments show the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 896–935, 2016 |
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| Keywords: | completely monotonic convolution kernel time discretization Volterra evolutionary integral equation weighted
convergence behavior |
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