Islamic Azad University Arak BranchJournal of Solid Mechanics2008-35058320160920Exact Implementation of Multiple Initial Conditions in the DQ Solution of Higher-Order ODEs540559524269ENS.A EftekhariYoung Researchers and Elite Club, Karaj Branch, Islamic Azad UniversityJournal Article20160610The 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 <em>r</em>th order ordinary differential equation is “<em>m</em> + <em>r</em> – 1,” where <em>m</em> 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 “<em>m</em> – 1.” Some test problems are also provided to highlight the superiority of the proposed method over the CBCGE and MWCM approaches.http://jsm.iau-arak.ac.ir/article_524269_1684905d3c7064b67a2a0e3a00835fa8.pdf