Advanced Differential Quadrature Methods (Chapman & Hall/CRC by Zhi Zong

By Zhi Zong

The ebook was once very fascinating for me as my PhD thesis are hooked up with differential quadrature (DQ). It includes fairly new informations approximately improveing of the DQM. It base on authors articles from numerous final years. The detrimental is that the articles are shorten, so occasionally you should search for them within the booklet info base to discover info. occasionally it isn't so transparent clarify from the place the autors receive there formulation [there could be extra references to literature] - occasionally it truly is attainable to discover theorems that healthy even beter to the topic. besides i'm more than happy to have this e-book because it offers me much convenient informations approximately instructions of the DQ thought boost.

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Extra resources for Advanced Differential Quadrature Methods (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)

Example text

It should be mentioned that each block is considered as an open box in the numerical computation. We proceed from block 1 (BLK1). For this block, the function values at the bottom boundary (t = 0) are given from the initial condition. The function values at interior points and the top boundary (t = δt1 ) are considered as unknowns, which are given from the solution to Eq. 56). After obtaining the solution in BLK1, we march to BLK2, where the bottom boundary (t = δt1 ) is exactly the same as the top boundary of BLK1.

802 s. The above test cases show that the increase of δt and the proper choice of L can enhance the efficiency of block-marching technique 30 Advanced Differential Quadrature Methods while keeping the high order of accuracy for numerical results. However, it should be noted that there is a limitation on the choice of δt. If δt is too large, the accuracy of numerical results can be greatly reduced if L is not large enough. 8, where t is taken as 5 and L is chosen as 13 and 21 respectively. Only four blocks are involved in this case.

Shu (2000a) has proven that Eqs. 35) is (N − 1)-th order accurate, and thus it can yield very accurate results using a significantly small number of nodes. But Eqs. 43) are sensitive to how nodes are distributed. If nodes are uniformly distributed, it does not converge to the true function as N → ∞. 3 through Runge example. So, uniform spacing of nodes may lead to disastrous consequences. Among non-uniform spacing of nodes which ensure the convergence of Eqs. 43), the Chebyshev nodes defined by Eq.

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