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Equadiff 6 pp 275-284 | Cite as

Stability and error estimates valid for infinite time, for strongly monotone and infinitely stiff evolution equations

  • O. Axelsson
Lectures Presented In Sections Section C Numerical Methods
Part of the Lecture Notes in Mathematics book series (LNM, volume 1192)

Abstract

For evolution equation with a monotone operator we derive unconditional stability and error estimates valid for all times. θ-method, For the θ=1/2(2+ζτV), 0<v≤1, ζ>0), we prove an error estimate O(τ4/3), τ → 0, if V=1/3, where τ is the maximal timestep for an arbitrary choice of the sequence of timesteps and with no further condition on F, and an estimate O(τ2) under some additional conditions. The first result is an improvement over the implicit midpoint method (θ=½), for which an order reduction to O(τ) may occur.

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Copyright information

© Equadiff 6 and Springer-Verlag 1986

Authors and Affiliations

  • O. Axelsson
    • 1
  1. 1.Department of MathematicsUniversity of Nijmegen ToernooiveldNijmegenThe Netherlands

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