Abstract
We study discretization in classes of integro-differential equations
, where the functions a j (t), 1 ⩽ j ⩽ n, are completely monotonic on (0,∞) and locally integrable, but not constant. The equations are discretized using the backward Euler method in combination with order one convolution quadrature for the memory term. The stability properties of the discretization are derived in the weighted l 1(ρ; 0,∞) norm, where ρ is a given weight function. Applications to the weighted l 1 stability of the numerical solutions of a related equation in Hilbert space are given.
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Xu, D. The time discretization in classes of integro-differential equations with completely monotonic kernels: Weighted asymptotic stability. Sci. China Math. 56, 395–424 (2013). https://doi.org/10.1007/s11425-012-4410-2
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DOI: https://doi.org/10.1007/s11425-012-4410-2
Keywords
- the classes of integro-differential equation
- completely monotonic kernel
- backward Euler method
- convolution quadrature
- weighted l 1 asymptotic stability