Spline-based differential quadrature for fourth order differential equations and its application to Kirchhoff plates.

*(English)*Zbl 1046.65063Summary: A quintic B-spline-based differential quadrature method (SDQM) is developed to deal with fourth order differential equations. With the construction of cardinal spline interpolations using the normalized quintic B-spline functions, explicit expressions of weighting coefficients for approximation of derivatives are obtained. Some bending, buckling problems of the Kirchhoff plate characterized by fourth order differential equations are studied using the method. Very good agreement with other available solutions is reached. Numerical results show that the newly constructed spline-based differential quadrature is more versatile than the conventional differential quadrature. The present spline-based differential quadrature is found to be an effective alternative to the conventional differential quadrature.

##### MSC:

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

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74K20 | Plates |

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

##### Keywords:

Differential quadrature method; Spline-based differential quadrature method; Weighting coefficients; Numerical results; quintic B-spline functions; Kirchhoff plate
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\textit{H. Zhong}, Appl. Math. Modelling 28, No. 4, 353--366 (2004; Zbl 1046.65063)

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