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Characteristics of the Differential Quadrature Method and Its Improvement
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The differential quadrature method has been widely used in scientific and engineering computation. However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions. In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the importantV-transformation feature. Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable ands-stages-order method. On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method ofs-stage 2s-order have been proposed by using undetermined coefficients method and Padé approximations. The numerical results show that the improved differential quadrature method is more precise than the traditional differential quadrature method.
Title: Characteristics of the Differential Quadrature Method and Its Improvement
Description:
The differential quadrature method has been widely used in scientific and engineering computation.
However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions.
In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the importantV-transformation feature.
Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable ands-stages-order method.
On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method ofs-stage 2s-order have been proposed by using undetermined coefficients method and Padé approximations.
The numerical results show that the improved differential quadrature method is more precise than the traditional differential quadrature method.
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