Determination of the weighting coefficients for differential quadrature method based on spline interpolation

Artur Krowiak


The paper deals with the methodology of the determination of the weighting coefficients for differential quadrature method based on spline interpolation. Appropriate formulas are derived and two practical approaches to determine mentioned coefficients are proposed, one – pure numeric, the other that uses symbolic-numeric programming. Both approaches are analyzed on account of efficiency, conditioning of the problem and easiness of the implementation.

Słowa kluczowe: differential quadrature method, spline interpolation, weighting coefficients

Bert C.W., Malik M., Differential quadrature method in computational mechanics, Applied Mechanics Review, 49, 1996, 1-28.

Shu C., Richards B.E., Application of generalized differential quadrature to solve two-dimensional incompressible Nanier-Stokes equations, International Journal for Numerical Methods in Fluids, 15, 1992, 791-798.

Shu C., Differential quadrature and its application in engineering, Springer-Verlag, London, 2000.

Krowiak A., The application of the differential quadrature method based on a piecewise polynomial to the vibration analysis of geometrically nonlinear beams, Computer Assisted Mechanics and Engineering Sciences, 15, 2008, 1-13.

Zong Z., A variable order approach to improve differential quadrature accuracy in dynamic analysis, Journal of Sound and Vibration, 266, 2003, 307-323.

Krowiak A., Symbolic computing in spline-based differential quadrature method, Communications in Numerical Methods in Engineering, 22, 2006, 1097-1107.