Summary
In this paper Lie series are presented in Chebyshev form and applied to the iterative solution of initial value problems in differential equations. The resulting method, though algebraically complicated, is of theoretical interest as a generalisation of Taylor series methods and iterative Chebyshev methods. The theory of the method is discussed and the solutions of some simple scalar equations are analysed to illustrate the behaviour of the process.
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References
Grobner, W., Knapp, H.: Contribution to the method of Lie series. B.I.Hochschultaschenbücher 802/802a. Mannheim: Bibliographisches Institut 1967
Householder, A.S.: The numerical treatment of a single nonlinear equation, p. 73. New York: McGraw-Hill 1970
Knapp, H., Wanner, G.: Numerical solution of differential equations by Grobner's method of Lie series. MRC Techn. sum. Rep. 880, Mathematics Research Centre, Univ. Wisconsin, Madison. (1968)
Stetter, H.J.: Analysis of discretization methods for ordinary differential equations. Berlin-Heidelberg-New York: Springer 1973
Urabe, M.: The Newton method and its application to boundary value problems with non-linear boundary conditions. Proceedings of Japan American Symposium. New York: Benjamin 1967
Wright, K.: Chebyshev collocation methods for ordinary differential equations. Comp. J. Vol.6, 358–365 (1964)
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Greig, D.M., Abd-el-Naby, M.A. Iterative solutions of nonlinear initial value differential equations in Chebyshev series using Lie series. Numer. Math. 34, 1–13 (1980). https://doi.org/10.1007/BF01463994
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DOI: https://doi.org/10.1007/BF01463994