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**Rational Chebyshev tau method for solving higher-order ordinary differential equations.**
*(English)*
Zbl 1047.65052

Summary: An approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev (RC) tau method. The operational matrices of the derivative and product of RC functions are presented. These matrices together with the tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

### MSC:

65L05 | Numerical methods for initial value problems involving ordinary differential equations |

34A30 | Linear ordinary differential equations and systems |

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

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\textit{K. Parand} and \textit{M. Razzaghi}, Int. J. Comput. Math. 81, No. 1, 73--80 (2004; Zbl 1047.65052)

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### References:

[1] | Evans D. J. (1968)The Use of Preconditioning in Iterative Methods for Solving Linear Equations with SPD MatricesJ.I.M.A. pp. 293–314 |

[2] | Evans D. J. (1973) The analyses and application of sparse matrix algorithms in the finite element method The Mathematics of Finite Elements and Applic. Conf. Proc., April 1972. J. R. Whiteman (Ed.) Academic Press London pp. 427–447 |

[3] | Evans D. J., Preconditioned Iterative Methods (1994) · Zbl 0832.65025 |

[4] | Evans D. J., Preconditioning Methods: Theory and Applications pp pp. 69–80– (1983) |

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