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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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