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Spline-based differential quadrature for fourth order differential equations and its application to Kirchhoff plates. (English) Zbl 1046.65063
Summary: 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
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