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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Uniform $l^{1}$ convergence in the Crank-Nicolson method of a linear integro-differential equation for viscoelastic rods and plates
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by Da Xu PDF
Math. Comp. 83 (2014), 735-769 Request permission


We study the numerical approximation of a certain Volterra integro-differential equation in Hilbert space which arises in the linear theory of isotropic viscoelastic rods and plates. The equation is discretized in time using a method based on the trapezoidal rule: while the time derivative is approximated by the trapezoidal rule in a two-step method, a convolution quadrature rule, constructed again from the trapezoidal rule, is used to approximate the integral term. The resulting scheme is shown to be convergence in the $l_{t}^{1}(0,\infty ;H)\bigcap l_{t}^{\infty }(0,\infty ; H)$ norm.
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Additional Information
  • Da Xu
  • Affiliation: Department of Mathematics, Hunan Normal University, Changsha 410081, Hunan, People’s Republic of China
  • Email:
  • Received by editor(s): January 22, 2011
  • Received by editor(s) in revised form: June 5, 2012
  • Published electronically: September 5, 2013
  • Additional Notes: This work was supported in part by the National Natural Science Foundation of China, contract grant numbers 11271123, 10971062.
  • © Copyright 2013 American Mathematical Society
  • Journal: Math. Comp. 83 (2014), 735-769
  • MSC (2010): Primary 65J08, 65D32; Secondary 45K05
  • DOI:
  • MathSciNet review: 3143690