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Numerical techniques for nonlinear multi-parameter problems

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Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1066))

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References

  1. Bauer, L., Reiss, E.L. and Keller, H.B. Axisymmetric buckling of hollow spheres and hemispheres, Comm. Pure and Appl. Math. 23, (1970), pp 529–568.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bazley, N.W. and Wake, G.C. The disappearance of criticality in the theory of thermal ignition. ZAMP 29 (1979) pp 971–976.

    Article  Google Scholar 

  3. Benjamin, T.B. Bifurcation phenomena in steady flows of a visicous fluid I. Theory Proc. R. Soc. Lond. A, 359 (1977), pp 1–26: II. Experiments Proc. R. Soc. Lond. A. 359 (1977), pp 27–43

    Article  MathSciNet  Google Scholar 

  4. Bigge, J. and Bohl, E. On the steady states of finitely many chemical cells. Preprint of the University of Konstanz (1982).

    Google Scholar 

  5. Boddington, T., Gray, P. and Robinson, C. Thermal explosions and the disappearance of criticality at small activation energies: exact results for the slab. Proc. R. Soc. Lond. A 368, (1979) pp 441–468.

    Article  Google Scholar 

  6. Cliffe, K.A. Numerical calculation of two-cell and single-cell Taylor flows, J. Fluid Mech. (to appear).

    Google Scholar 

  7. Crandall, M.G. and Rabinowitz, P.H. Bifurcation, perturbation of simple eigenvalues and linearised stability. Arch. Rat. Mech. Anal. 52 (1973) pp 161–180.

    Article  MathSciNet  MATH  Google Scholar 

  8. Decker, D.W. and Keller, H.B. Path following near bifurcation. Comm. Pure Appl. Math. 34 (1981) pp 149–175.

    Article  MathSciNet  MATH  Google Scholar 

  9. Ermentrout, G.B. and Cowen, J.D. Secondary bifurcation in neuronal nets. SIAM J. Appl Math. 39 (1980), pp 323–340.

    Article  MathSciNet  MATH  Google Scholar 

  10. Golubitsky, M. and Schaeffer, D. A theory for imperfect bifurcation via singularity thoery. Comm Pure Appl. Math. 32 (1979), pp 21–98.

    Article  MathSciNet  MATH  Google Scholar 

  11. Heinemann, R.F. and Poore, A.B. Multiplicity, stability and oscillatory dynamics of the tubular reactor. Chem. Eng. Sci. 36 (1981) pp 1411–1419.

    Article  Google Scholar 

  12. Jepson, A. and Spence, A. Folds in solutions of two-parameter systems: Part I, Tech. Rep. NA-82-02, Computer Science Department, Standford Univ. Stanford, CA, (1982), submitted to SIAM JNA

    Google Scholar 

  13. Jepson, A. and Spence, A. The numerical solution of nonlinear equations having several parameters Part I: Scalar Equations (1983) (submitted)

    Google Scholar 

  14. Keller, H.B. Numerical solution of bifurcation and nonlinear eigenvalue problems. In "Applications of Bifurcation Theory" ed½ P.H. Rabinowitz, Academic Press, New York, (1977), pp 359–384.

    Google Scholar 

  15. Keller, H.B. and Szeto, R.K-H. Calculation of flows between rotating disks, in "Computing Methods in Applied Sciences and Engineering" ed. R. Glowinski and J.L. Lions (1980) pp 51–61 (North Holland).

    Google Scholar 

  16. Keller, H.B. Singular systems, inverse iteration and least squares. (Private communication)

    Google Scholar 

  17. Rheinboldt, W.C. Computation of critical boundaries on equilibrium manifolds SIAM J. Numer. Anal. 19 (1982) pp 653–669.

    Article  MathSciNet  MATH  Google Scholar 

  18. Rheinboldt, W.C. and Burkardt, J.V. A locally parameterized continuation process ACM TOMS, 9 (1983) pp 215–235.

    Article  MathSciNet  MATH  Google Scholar 

  19. Schaeffer, D.G. Qualitative analysis of a model for boundary effects in the Taylor problem. Math. Proc. Camb. Phil. Soc. 87, (1980) pp 307–337.

    Article  MathSciNet  MATH  Google Scholar 

  20. Spence, A. and Jepson, A. The numerical computation of turning points of nonlinear equations, in "Treatment of integral equations by Numerical Methods" ed. C.T.H. Baker, G.F. Miller, Academic Press, London, (1982) pp 169–183.

    Google Scholar 

  21. Spence, A. and Werner, B. Non-simple turning points and cusps. IMA J. Num. Anal. 2, (1982) pp 413–427.

    Article  MathSciNet  MATH  Google Scholar 

  22. Uppal, A., Ray, W.H. and Poore, A.B. The classification of the dynamic behaviour of continuous stirred tank reactors — influence of reactor residence time. Chem. Eng. Sci. 31 (1976) pp 205–214.

    Article  Google Scholar 

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David F. Griffiths

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© 1984 Springer-Verlag

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Spence, A., Jepson, A. (1984). Numerical techniques for nonlinear multi-parameter problems. In: Griffiths, D.F. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 1066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099524

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  • DOI: https://doi.org/10.1007/BFb0099524

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  • Print ISBN: 978-3-540-13344-5

  • Online ISBN: 978-3-540-38881-4

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