Uniform l1 behaviour for time discretization of a Volterra equation with completely monotonic kernel: I. stability |
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Authors: | Da Xu |
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Institution: |
1 Department of Mathematics, Hunan Normal University, Changsha 410081, Hunan, People's Republic of China
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Abstract: | This paper is the first of two papers on the time discretizationof the equation ut + t 0 ß (t s) Au (s) ds= 0, t > 0, u (0) = u0, where A is a self-adjoint denselydefined linear operator on a Hilbert space H with a completeeigensystem { m, m} m = 1, and ß (t) is completely monotonicand locally integrable, but not constant. The equation is discretizedin time using first-order differences in combination with order-oneconvolution quadrature. The stability properties of the timediscretization are derived in the l1t (0, ; H) norm. |
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Keywords: | Volterra equation completely monotonic kernel time discretization l1 stability |
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