A Test for Instability in the Numerical Solution of Ordinary Differential Equations

ABSTRACT

A procedure is described to test the individual components of the numerical solution to a system of differential equations for relative instability. Although the test is based on the theory for linear differential equations, it has also worked for nonlinear problems. Extra computation is negligible; the test involves checking the signs of previously computed numbers

REFERENCES

• 1: P. E. Chase, Stability Properties of Predictor-Corrector Methods for Ordinary Differential Equations, Journal of the ACM (JACM), v.9 n.4, p.457-468, Oct. 1962 [doi>10.1145/321138.321143]
• 2: R. L. Crane , R. W. Klopfenstein, A Predictor-Corrector Algorithm with an Increased Range of Absolute Stability, Journal of the ACM (JACM), v.12 n.2, p.227-241, April 1965 [doi>10.1145/321264.321272]
• 3: Fred T. Krogh, Predictor-Corrector Methods of High Order With Improved Stability Characteristics, Journal of the ACM (JACM), v.13 n.3, p.374-385, July 1966 [doi>10.1145/321341.321347]
• 4: NORDSlECK, A., On numerical integration of ordinary differential equations. Math. Comput 16 (1962), 22-49.
• 5: STETTER, H. J. Stabilizing predictors for weakly unstable correctors. Math. Comput. It (1965), 84-89.
• 6: -- A study of strong and weak stability in diseretization algorithms. J. SIAM Numer Anal. Ser. B 2 (1965), 265--280.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.7 Ordinary Differential Equations
          Subjects: Convergence and stability

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

General Terms:
Algorithms, Performance, Reliability, Theory