Chebyshev finite difference approximation for the boundary value problems.

*(English)*Zbl 1027.65098Summary: This paper presents a numerical technique for solving linear and non-linear boundary value problems for ordinary differential equations. This technique is based on using matrix operator expressions which applies to the differential terms. It can be regarded as a non-uniform finite difference scheme. The values of the dependent variable at the Gauss-Lobatto points are the unknown one solves for.

The application of the method to boundary value problems leads to algebraic systems. The method permits the application of iterative method in order to solve the algebraic systems. The effective application of the method is demonstrated by four examples.

The application of the method to boundary value problems leads to algebraic systems. The method permits the application of iterative method in order to solve the algebraic systems. The effective application of the method is demonstrated by four examples.

##### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

65L12 | Finite difference and finite volume methods for ordinary differential equations |

34B05 | Linear boundary value problems for ordinary differential equations |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

##### Keywords:

Chebyshev approximation; boundary value problems; incomplete LU-decomposition; numerical examples; non-uniform finite difference scheme; iterative method
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\textit{E. M. E. Elbarbary} and \textit{M. El-Kady}, Appl. Math. Comput. 139, No. 2--3, 513--523 (2003; Zbl 1027.65098)

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