Solution of nonlinear initial-value problems by the spline-based differential quadrature method

Journal of Sound and Vibration

Volumn 296, Issue 4-5, 2006, Pages 908-918

  Zhong, Hongzhi ^a   Lan, Mengyu ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CONTROL NONLINEARITIES; DIFFERENTIAL EQUATIONS; INTEGRATION; NUMERICAL METHODS; PROBLEM SOLVING;

DYNAMIC SYSTEMS; SPLINE-BASED DIFFERENTIAL QUADRATURE METHOD (SDQM); WEIGHTING COEFFICIENTS;

INITIAL VALUE PROBLEMS;

EID: 33745978054     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2006.03.018     Document Type: Article

References (18)

1. Bert C.W., and Malik M. Differential quadrature method in computational mechanics: a review. Applied Mechanics Reviews 49 (1996) 1-27
2. Shu C. Differential Quadrature and its Application in Engineering (2000), Springer, London
3. Bellman R.E., and Casti J. Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications 34 (1971) 235-238
4. Fung T.C. Stability and accuracy of differential quadrature method in solving dynamics problems. Computer Methods in Applied Mechanics and Engineering 191 (2002) 1311-1331
5. Chen W., and Tanaka M. A study on time schemes for DRBEM analysis of elastic impact wave. Computational Mechanics 28 (2002) 331-338
6. Wu T.Y., and Liu G.R. The generalized differential quadrature rule for initial-value differential equations. Journal of Sound and Vibration 233 (2000) 195-213
7. Liu G.R., and Wu T.Y. Numerical solution for differential equations of Duffing-type non-linearity using the generalized differential quadrature. Journal of Sound and Vibration 237 (2000) 805-817
8. Shu C., Yao Q., and Yeo K.S. Block-marching in time with DQ discretization: an efficient method for time-dependent problems. Computer Methods in Applied Mechanics and Engineering 191 (2002) 4587-4597
9. Fung T.C. Solving initial value problems by differential quadrature method-Part Two: second- and higher-order equations. International Journal for Numerical Methods in Engineering 50 (2001) 1429-1454
10. Tomasiello S. Simulating non-linear coupled oscillators by an iterative differential quadrature method. Journal of Sound and Vibration 265 (2003) 507-525
11. Zhong H. Spline-based differential quadrature for fourth order differential equations and its application to Kirchhoff plates. Applied Mathematical Modelling 28 (2004) 353-366
12. Zhong H., and Guo Q. Vibration analysis of rectangular plates with free corners using spline-based differential quadrature. Shock and Vibration 11 (2004) 119-128
13. Schultz M.H. Spline Analysis (1973), Prentice-Hall, Englewood Cliffs, NJ
14. Schumaker L.L. Spline Functions: Basic Theory (1981), Wiley, New York
15. Li Y.S., and Qi D.X. Spline Function Method (1979), Science Press, Beijing (in Chinese)
16. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (1987), Prentice-Hall, Englewood Cliffs, NJ
17. Groves Jr. F.R. Numerical solution of nonlinear differential equations using computer algebra. International Journal of Computer Mathematics 13 (1983) 301-309
18. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical Recipes-The Art of Scientific Computing (1986), Cambridge University Press, Cambridge