Application of the generalized differential quadrature rule to initial - Boundary-value problems

Journal of Sound and Vibration

Volumn 264, Issue 4, 2003, Pages 883-891

  Wu, T Y ^a   Liu, G R ^b   Wang, Y Y ^a  

^a INSTITUTE OF HIGH PERFORMANCE COMPUTING   (Singapore)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

BEAMS AND GIRDERS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; VIBRATIONS (MECHANICAL);

DIFFERENTIAL QUADRATURE METHOD (DQM);

BOUNDARY VALUE PROBLEMS;

EID: 0038036099     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-460X(02)01195-1     Document Type: Article

References (20)

1. R. Bellman, J. Casti, Differential quadrature and long term integration, Journal of Mathematical Analysis and Applications 34 (1971) 235-238.
2. R. Bellman, B.G. Kashef, J. Casti, Differential quadrature: a technique for the rapid solution of non-linear partial differential equations, Journal of Computational Physics 10 (1972) 40-52.
3. S. Temasiello, Differential quadrature method: application to initial-boundary-value problems, Journal of Sound and Vibration 218 (1998) 573-585.
4. T.Y. Wu, G.R. Liu, The generalized differential quadrature rule for initial value differential equations, Journal of Sound and Vibration 233 (2000) 195-213.
5. G.R. Liu, T.Y. Wu, Numerical solution for differential equations of Duffing-type non-linearity using the generalized differential quadrature rule, Journal of Sound and Vibration 237 (2000) 805-817.
6. T.Y. Wu, G.R. Liu, The differential quadrature as a numerical method to solve the differential equation, Computational Mechanics 24 (1999) 197-205.
7. T.Y. Wu, G.R. Liu, The generalized differential quadrature rule for fourth-order differential equations, International Journal for Numerical Methods in Engineering 50 (2001) 1909-1929.
8. T.Y. Wu, G.R. Liu, Application of the generalized differential quadrature rule to sixth-order differential equations, Communications in Numerical Methods in Engineering 16 (2000) 777-784.
9. T.Y. Wu, G.R. Liu, Application of the generalized differential quadrature rule to eighth-order differential equations, Communications in Numerical Methods in Engineering 17 (2001) 355-364.
10. G.R. Liu, T.Y. Wu, An application of the generalized differential quadrature rule in Blasius and Onsager equations, International Journal for Numerical Methods in Engineering 52 (2001) 1013-1027.
11. G.R. Liu, T.Y. Wu, Multipoint boundary value problems by the differential quadrature method, Mathematical and Computer Modelling 35 (2002) 215-227.
12. M.L. Michelsen, J. Villadsen, Aconvenient computational procedure for collocation constants, The Engineering Chemical Journal 4 (1972) 64-68.
13. J. Villadsen, M.L. Michelsen, Solution of Differential Equation Models by Polynomial Approximation, Prentice- Hall, Engelwood Cliffs, NJ, 1978.
14. J.R. Quan, C.T. Chang, New insights in solving distributed system equations by the differential quadrature method - I: analysis, Computers and Chemical Engineering 13 (1998a) 779-788.
15. J.R. Quan, C.T. Chang, New insights in solving distributed system equations by the differential quadrature method - II: numerical experiments, Computers and Chemical Engineering 13 (1999b) 1017-1024.
16. C. Shu, Differential Quadrature and its Application in Engineering, Springer, London, 2000.
17. S.S. Rao, Mechanical Vibrations, 3rd Edition, Addison-Wesley, Reading, MA, USA, 1995.
18. T.Y. Wu, Y.Y. Wang, G.R. Liu, Free vibration analysis of circular plates using generalized differential quadrature rule, Computer Methods in Applied Mechanics and Engineering 191 (2002) 5365-5380.
19. T.Y. Wu, G.R. Liu, Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule, International Journal of Solids and Structures 38 (2001) 7967-7980.
20. G.R. Liu, T.Y. Wu, Differential quadrature solutions of eighth-order boundary-value differential equations. Journal of Computational and Applied Mathematics 145 (2002) 223-235.