Renormalized Coordinate Stretching: A Generalization of Shoot and Fit with Application to Stellar Structure

Show more

References

[1] C. B. Haselgrove and F. Hoyle, “A Mathematical Discussion of the Problem of Stellar Evolution, with Reference to the Use of an Automatic Digital Computer,” Monthly Notices of the Royal Astronomical Society, Vol. 116, 1956, pp. 515-526.

[2] W. H., Press, S. A., Teukolsky, W. T. Vetterling and B. P. Flannery, “Numerical Recipes,” Cambridge University Press, Cambridge, 2007.

[3] S. M. Roberts and J. S. Shipman, “Two-Point Boundary Value Problems: Shooting Methods,” Elsevier, New York, 1972.

[4] A. Lindstedt, “Ueber Die Integration Einer Für Die Str?rungstheorie Wichtigen Differentialgleichung,” Astronomische Nachrichten, Vol. 103, No. 14, 1882, pp. 211-220.

[5] H. Poincaré, “Les Méthodes Nouvelles de la Méchanique Céleste,” Gauthier-Villars, Paris, 1892.

[6] M. J. Lighthill, “A Technique for Rendering Approximate Solutions to Physical Problems Uniformly Convergent,” Philosophical Magazine, Vol. 40, 1949, pp. 1179-1201.

[7] A. S. Nayfeh, “Perturbation Methods,” Wiley, New York, 2000. doi:10.1002/9783527617609

[8] J. Kevorkian and J. D. Cole, “Perturbation Methods in Applied Mathematics,” Springer Verlag, New York, 2010.

[9] M. Pritulo, “On the Determination of Uniformly Accurate Solutions of Differential Equations by the Method of Perturbation of Coordinates,” Journal of Applied Mathematics and Mechanics, Vol. 26, No. 3, 1962, pp. 661-667.
doi:10.1016/0021-8928(62)90034-5

[10] P. D. Usher, “Some New Algorithms for Stellar Structure,” Ph.D. Thesis, Harvard University, Harvard, 1966.

[11] S. Dai, “Poincaré-Lighthill-Kuo Method and Symbolic Computation,” Applied Mathematics and Mechanics, Vol. 22, No. 3, 2001, pp. 261-269. doi:10.1023/A:1015565502306

[12] J. Reiter, R. Bulirsch and J. Pfleiderer, “A Multiple Shooting Approach for the Numerical Treatment of Stellar Structure and Evolution,” Astronomische Nachrichten, Vol. 315, No. 3, 1994, pp. 205-234.
doi:10.1002/asna.2103150304

[13] B. L. Smith, “Strained Coordinate Methods in Rotating Stars,” Astrophysics and Space Science, Vol. 47, No. 1, 1977, pp. 61-78.

[14] M. Schwarzschild and R. H?rm, “Evolution of Very Massive Stars,” Astrophysical Journal, Vol. 128, 1958, pp. 348-360.

[15] R. Stothers, “Evolution of O Stars. I. Hydrogen-Burning,” Astrophysical Journal, Vol. 138, 1963, pp. 1074-1084.

[16] B. Maxfield, “Essential Mathcad,” Academic Press, Burlington, 2007.