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

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EFTEKHARI S.A.

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Journal Paper

Paper Information

Journal: JOURNAL OF SOLID MECHANICS Year:2016 | Volume:8 | Issue:3 Page(s): 540-559

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Information Journal Paper

Title

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

Author(s)

EFTEKHARI S.A. | Issue Writer Certificate

Keywords

NEW DIFFERENTIAL QUADRATURE METHODOLOGY

IMPOSING MULTIPLE INITIAL CONDITIONS

HIGHER-ORDER INITIAL-VALUE PROBLEMS

CBCGE APPROACH

MWCM APPROACH

BEAMS

RECTANGULAR PLATES

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

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APA: Copy

EFTEKHARI, S.A.. (2016). EXACT IMPLEMENTATION OF MULTIPLE INITIAL CONDITIONS IN THE DQ SOLUTION OF HIGHER-ORDER ODES. JOURNAL OF SOLID MECHANICS, 8(3), 540-559. SID. https://sid.ir/paper/319426/en

Vancouver: Copy

EFTEKHARI S.A.. EXACT IMPLEMENTATION OF MULTIPLE INITIAL CONDITIONS IN THE DQ SOLUTION OF HIGHER-ORDER ODES. JOURNAL OF SOLID MECHANICS[Internet]. 2016;8(3):540-559. Available from: https://sid.ir/paper/319426/en

IEEE: Copy

S.A. EFTEKHARI, “EXACT IMPLEMENTATION OF MULTIPLE INITIAL CONDITIONS IN THE DQ SOLUTION OF HIGHER-ORDER ODES,” JOURNAL OF SOLID MECHANICS, vol. 8, no. 3, pp. 540–559, 2016, [Online]. Available: https://sid.ir/paper/319426/en

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