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An algorithm for computing unstable solutions of semilinear boundary value problems

Ein Algorithmus zur Berechnung instabiler Lösungen halblinearer Randwertprobleme

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Abstract

We present a partially interactive algorithm for accurate computation of unstable solutions of semilinear Dirichlet boundary value problems.

Zusammenfassung

Wir stellen einen teilweise interaktiven Algorithmus zur genauen Berechnung instabiler Lösungen von halblinearen Dirichlet-Randwertproblemen vor.

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References

  1. Allgower, E. L., Chien, C. S., Georg, K.: Large sparse continuation problems. In: Mittelmann, H. D., Roose, D. (eds.) Continuation techniques and bifurcation problems, pp. 3–21. Boston: Birkhäuser, 1990.

    Google Scholar 

  2. Choudury, G., Korman, P.: On computation of solutions of fully nonlinear elliptic problems. J. Comp. Appl. Math.41, 301–311 (1992).

    Google Scholar 

  3. Henry, D.: Geometric theory of semilinear parabolic equations. Berlin, Heidelberg, New York: Springer 1981 (Lecture Notes in Mathematics,840).

    Google Scholar 

  4. Huy, C. U., McKenna, P. J., Walter, W.: Finite difference approximations to the Dirichlet problem for elliptic systems. Numer. Math.49, 227–237 (1986).

    Google Scholar 

  5. Korman, P.: On computation of solutions of elliptic systems. Numer. Funct. Anal. Optimiz.10, 977–990 (1989).

    Google Scholar 

  6. Luning, C. D., Perry, W. L.: Positive solutions of negatative exponent generalized Emden-Fowler boundary value problems. SIAM J. Math. Anal.12 (6), 874–879 (1981).

    Google Scholar 

  7. Rabinowitz, P. H.: Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. in Math. No. 65, Amer. Math. Soc., Providence, RI (1986).

  8. Sattinger, D. H.: Monotone methods in nonlinear elliptic and parabolic boundary value problems. Indiana Univ. Math. J.21, 979–1000 (1972).

    Google Scholar 

  9. Smiley, M. W.: A numerical study of spontaneous bifurcation. J. Comp. Appl. Math.19, 179–188 (1987).

    Google Scholar 

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Korman, P. An algorithm for computing unstable solutions of semilinear boundary value problems. Computing 51, 327–334 (1993). https://doi.org/10.1007/BF02238539

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  • DOI: https://doi.org/10.1007/BF02238539

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