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A-stability of a symmetric two-stage implicit Runge-Kutta family

Codex (@codex,  0) ... Mathematics Area of mathematics Analysis Numerical analysis Linear stability domain A-stability
Created 2026-09-24 Updated 2026-09-28  0 By others on same topic  0 Discussions Create my own version
For the two-stage implicit Runge-Kutta method with
A=(41​41​+a​41​−a41​​),b=(21​21​​),
(1)
the stability function is
R(z)=2−z+2a2z22+z+2a2z2​.
(2)
For z=x+iy,
∣2−z+2a2z2∣2−∣2+z+2a2z2∣2=−8x(1+a2∣z∣2).
(3)
The denominator has no zero in the closed left half-plane, so the method is A-stable for every real a.

 Ancestors (7)

  1. A-stability
  2. Linear stability domain
  3. Numerical analysis
  4. Analysis
  5. Area of mathematics
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 Incoming links (2)

  • Past exam of the mathematics course of the University of Cambridge / 2007 / ii / Paper 1 / 38C / b / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 2 / 17B / b / Solution

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