Paper Information

Journal:   JOURNAL OF SOLID MECHANICS   2016 , Volume 8 , Number 3; Page(s) 540 To 559.
 
Paper: 

EXACT IMPLEMENTATION OF MULTIPLE INITIAL CONDITIONS IN THE DQ SOLUTION OF HIGHER-ORDER ODES

 
 
Author(s):  EFTEKHARI S.A.*
 
* YOUNG RESEARCHERS AND ELITE CLUB, KARAJ BRANCH, ISLAMIC AZAD UNIVERSITY, KARAJ, IRAN
 
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

 
Keyword(s): NEW DIFFERENTIAL QUADRATURE METHODOLOGY, IMPOSING MULTIPLE INITIAL CONDITIONS, HIGHER-ORDER INITIAL-VALUE PROBLEMS, CBCGE APPROACH, MWCM APPROACH, BEAMS, RECTANGULAR PLATES
 
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