The time discretization in classes of integro-differential equations with completely monotonic kernels: Weighted asymptotic convergence (Q2808869)
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scientific article; zbMATH DE number 6584624
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The time discretization in classes of integro-differential equations with completely monotonic kernels: Weighted asymptotic convergence |
scientific article; zbMATH DE number 6584624 |
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The time discretization in classes of integro-differential equations with completely monotonic kernels: Weighted asymptotic convergence (English)
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25 May 2016
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completely monotonic convolution kernel
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time discretization
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Volterra evolutionary integral equation
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weighted \(l^1\) convergence
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integro-differential equations
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backward Euler method
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convolution quadrature
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numerical results
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The author studies the time discretization in classes of integro-differential equations with completely monotonic kernels and prove weighted asymptotic convergence. They use the backward Euler method combined with order one convolution quadrature for approximating the integral term and generalizes the results of \textit{D. Xu} [Sci. China, Math. 56, No. 2, 395--424 (2013; Zbl 1266.65212)]. Convergence properties of the time discretization are also given. Numerical results are given to illustrate the theory discussed.
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