Computational Methods for Differential Equations New Solutions for Singular Lane-Emden Equations Arising in As-trophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives

Waleed Abd-Elhameed, Youssri Youssri, Eid Doha
2014 unpublished
In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is built on transforming the equations with their initial conditions into systems of linear or nonlinear algebraic equations which can be
more » ... by using suitable numerical solvers. The Legendre and first and second kind Chebyshev operational matrices of derivatives can be deduced as special cases of the constructed operational matrices. For the sake of testing the validity and applicability of the suggested numerical algorithms, three illustrative examples are presented.
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