A new insight into the differential quadrature method in solving 2-D elliptic PDEs

CMES - Computer Modeling in Engineering and Sciences

Volumn 71, Issue 2, 2011, Pages 157-178

  Shen, Ying Hsiu ^a   Liu, Chein Shan ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Differential quadrature (DQ); Dirichlet boundary conditions; Elliptic Partial differential equations; Fictitious time integration method (FTIM); Vandermonde matrix

Indexed keywords

DIFFERENTIAL QUADRATURE; DIRICHLET BOUNDARY CONDITIONS; ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS; FICTITIOUS TIME INTEGRATION METHODS; VANDERMONDE MATRIX;

BOUNDARY CONDITIONS; DIFFERENTIATION (CALCULUS); GEOMETRY; INTEGRATION; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; TEST FACILITIES;

INTEGRAL EQUATIONS;

EID: 79955505709     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. Atluri, S. N.; Zhu, T. L. (1998a): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comp. Mech., vol. 22, pp. 117-127. (Pubitemid 128620889)
2. Atluri, S. N.; Zhu, T. L. (1998b): A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation. Comp. Model. Simul. Eng., vol. 3, pp. 187-196.
3. Bellman, R. E.; Casti, J. (1971): Differential quadrature and long-term integration. J. Math. Anal. Appl., vol. 34, pp. 235-238.
4. Bellman, R. E.; Kashef, B. G.; Casti, J. (1972): Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J. Comp. Phys., vol. 10, pp. 40-52.
5. Liu, C.-S. (2008): A fictitious time integration method for two-dimensional quasilinear elliptic boundary value problems. CMES: Computer Modeling in Engineering & Sciences, vol. 33, pp. 179-198.
6. Liu, C.-S. (2009): A fictitious time integration method for a quasilinear elliptic boundary value problem, defined in arbitrary plane domain. CMC: Computers, Materials & Continua, vol. 11, pp. 15-32.
7. Liu, C.-S.; Atluri, S. N. (2008): A novel time integration method for solving a large system of non-linear algebraic equations. CMES: Computer Modeling in Engineering & Sciences, vol. 31, pp. 71-83.
8. Liu, C.-S.; Hong, H. K.; Atluri, S. N. (2010): Novel algorithms based on the conjugate gradient method for inverting ill-conditioned matrices, and a new regularization method to solve ill-posed linear systems. CMES: Computer Modeling in Engineering & Sciences, vol. 60, pp. 279-308.
9. Quan, J. R.; Chang, C.-T. (1989a): New insights in solving distributed system equations by the quadrature methods-I. Comput. Chem. Eng., vol. 13, pp. 779-788. (Pubitemid 20620969)
10. Quan, J. R.; Chang, C.-T. (1989b): New insights in solving distributed system equations by the quadrature methods-II. Comput. Chem. Eng., vol. 13, pp. 1017-1024. (Pubitemid 20632558)
11. Shu, C. (2000): Differential Quadrature and its Applications in Engineering. Springer, Berlin.
12. Zhu, T.; Zhang, J.; Atluri, S. N. (1998): A meshless local boundary integral equation (LBIE) method for solving nonlinear problems. Comp. Mech., vol. 22, pp. 174-186. (Pubitemid 128620894)
13. Zhu, T.; Zhang, J.; Atluri, S. N. (1999): A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems. Eng. Anal. Bound. Elem., vol. 23, pp. 375-389.
14. Zong, Z.; Lam, K. Y. (2002): A localized differential quadrature (LDQ) method and its application to the 2D wave equation. Comput. Mech., vol. 29, pp. 382-391. (Pubitemid 35422278)