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.

##### MSC:

65L10 | Boundary value problems for ODE (numerical methods) |

65L12 | Finite difference methods for ODE (numerical methods) |

34B05 | Linear boundary value problems for ODE |

34B15 | Nonlinear boundary value problems for ODE |