Iterative solutions of nonlinear initial value differential equations in Chebyshev series using Lie series |
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Authors: | D M Greig M A Abd-el-Naby |
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Institution: | (1) Department of Mathematics, University or Durham, Science Laboratories, South Road, Durham, England;(2) Ain Shams University, Cairo, Egypt |
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Abstract: | 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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Keywords: | AMS(MOS): 34A45 34A50 65L05 CR: 5 17 |
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