Stiffness detection and estimation of dominant spectrum with explicit Runge-Kutta methods

ABSTRACT

A new stiffness detection scheme based on explicit Runge-Kutta methods is proposed. It uses a Krylov subspace approximation to estimate the eigenvalues of the Jacobian of the differential system. The numerical examples indicate that this technique is a worthwhile alternative to other known stiffness detection schemes, especially when the systems are large and when it is desirable to know more about the spectrum of the Jacobian than just the spectral radius.

REFERENCES

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Initial value problems

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Stiff equations; One-step (single step) methods

General Terms:
Algorithms

Keywords:
explicit Runge-Kutta method, stiffness detection