A note on the numerical solution of high-order differential equations.

*(English)*Zbl 1031.65087Summary: The numerical solution of high-order differential equations with multi-boundary conditions is discussed. Motivated by the discrete singular convolution algorithm, the use of fictitious points as additional unknowns is proposed in the implementation of locally supported Lagrange polynomials. The proposed method can be regarded as a local adaptive differential quadrature method. Two examples, an eigenvalue problem and a boundary-value problem, which are governed by a sixth-order differential equation and an eighth-order differential equation, respectively, are employed to illustrate the proposed method.

##### MSC:

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

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

34L16 | Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators |

65L15 | Numerical solution of eigenvalue problems involving ordinary differential equations |

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

##### Keywords:

High-order differential equation; Multi-boundary conditions; Local adaptive differential quadrature method; numerical examples; eigenvalue problem; boundary-value problem
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\textit{Y. Wang} et al., J. Comput. Appl. Math. 159, No. 2, 387--398 (2003; Zbl 1031.65087)

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##### References:

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