| The differential quadradure (DQ) method is a distinct numerical solution technique withadvantages of conceptual simplicity, high accuracy and relatively small computing effort. The method itself has been extensively studied and matured. In the aspect of applications, the DQ method has been usually applied to solve boundary value problems. In this thesis, the study is focused on solving intial value problems by using the DQ method. A step-by-step time integration algorithm based on the differential quadrature method with a special type of grid points is introduced first. Through theoretical analysis and numerical experiment, the DQ based integration algorithm and other commonly used time integration schemes are compared. Then both linear and nonlinear examples are solved numerically. The results by various integration schemes are compared each other. It is shown that the DQ based time integration method has the advantages of unconditional stability, high accuracy and controllable numerical dissipation in high-frequecy ranges, and that no"overshoot"occurs. In the low-frequecy ranges, the numerical dissipation of the DQ method is the smallest among all algorithms studied. Accurate results could be obtained by the DQ method with much larger time step than other algorithms, thus the method is especially suitable for long-term integration. In high-frequecy ranges, the algorithm based on DQ method is asymptotic annihilation when the parameter is choosen asμ= 0, which could help to damp out the spurious high-frequecy responses often encountered when using the finite element method to discretize the spatial domain. When solving the nonlinear problems, accurate numerical results could also be obtained by using the DQ method with much larger time step over the commonly used time integration schemes. Based on the results reported herein, some conclusions are drawn. Some research topics for further research are also pointed out.
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