Exact Implementation of Multiple Initial Conditions in the DQ Solution of Higher-Order ODEs
Publish place: Journal of Solid Mechanics، Vol: 8، Issue: 3
Publish Year: 1395
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JSMA-8-3_006
تاریخ نمایه سازی: 12 اسفند 1398
Abstract:
The differential quadrature method (DQM) is one of the most elegant and useful approximate methods for solving initial and/or boundary value problems. It is easy to use and also straightforward to implement. However, the conventional DQM is well-known to have some difficulty in implementing multiple initial and/or boundary conditions at a given discrete point. To overcome this difficulty, this paper presents a simple and accurate differential quadrature methodology in which the higher-order initial conditions are exactly implemented. The proposed methodology is very elegant and uses a set of simple polynomials with a simple transformation to incorporate the higher-order initial conditions at the initial discrete time point. The order of accuracy of the proposed method for solving an rth order ordinary differential equation is m + r – 1, where m being the number of discrete time points. This is better than the accuracy of the CBCGE (direct Coupling the Boundary/initial Conditions with the discrete Governing Equations) and MWCM (Modifying Weighting Coefficient Matrices) approaches whose order is in general m – 1. Some test problems are also provided to highlight the superiority of the proposed method over the CBCGE and MWCM approaches.
Keywords:
New differential quadrature methodology , Imposing multiple initial conditions , Higher-order initial-value problems , CBCGE approach , MWCM approach , Beams , Rectangular plates
Authors
S.A Eftekhari
Young Researchers and Elite Club, Karaj Branch, Islamic Azad University
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