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An averaging method for the stiff highly oscillatory problem

Authors: W. L. Miranker and G. Wahba
Journal: Math. Comp. 30 (1976), 383-399
MSC: Primary 65L05
MathSciNet review: 0423817
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Abstract: We show how to replace the point functionals of numerical analysis with types of stable functionals of highly oscillatory solutions of differential equations. This replacement leads to the development of effective numerical methods for the stiff highly oscillatory problem.

References [Enhancements On Off] (What's this?)

  • [1] G. BJUREL et al., Survey of Stiff Ordinary Differential Equations, Royal Inst. Tech., Stockholm, Report NA 70.11.
  • [2] W. L. MIRANKER, "Matricial difference schemes for integrating stiff systems of ordinary differential equations," Math. Comp., v. 25, 1971, pp. 717-728. MR 46 #1094. MR 0301939 (46:1094)
  • [3] W. L. MIRANKER & F. HOPPENSTEADT, Numerical Methods for Stiff Systems of Differential Equations Related with Transistors and Tunnel Diodes, Lecture Notes in Computer Science, vol. 10, Springer-Verlag, Berlin and New York, 1974, pp. 413 ff. MR 0436601 (55:9544)
  • [4] A. D. SNIDER & G. C. FLEMING, "Approximation by aliasing with application to 'Certaine' stiff differential equations," Math. Comp., v. 28, 1974, pp. 465-473. MR 49 #8377. MR 0343637 (49:8377)
  • [5] Stiff Differential Systems, IBM Symposia Series, Plenum Press, New York, 1974. (Edited by R. A. Willoughby.) MR 0343619 (49:8359)
  • [6] V. AMDURSKY & A. ZIV, On the Numerical Treatment of Stiff, Highly Oscillatory Systems, IBM Israel Science Center, Report 015, Haifa, 1974.

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Article copyright: © Copyright 1976 American Mathematical Society

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