Applications of the fictitious time integration method using a new time-like function

CMES - Computer Modeling in Engineering and Sciences

Volumn 43, Issue 2, 2009, Pages 173-190

  Ku, C Y ^a   Yeih, Weichung ^a   Liu, C S ^b   Chi, C C ^a  

^a NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Boundary value problem; Fictitious time integration method (FTIM); Numerical method; Three dimensional; Time like function

Indexed keywords

CONTROL PARAMETERS; FICTITIOUS TIME INTEGRATION METHOD (FTIM); FICTITIOUS TIME INTEGRATION METHODS; HIGHLY NONLINEAR; NUMERICAL IMPLEMENTATION; TIME INTEGRATION;

CONTROL SYSTEM ANALYSIS; NUMBER THEORY; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; THREE DIMENSIONAL;

BOUNDARY VALUE PROBLEMS;

EID: 76249127210     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. Atluri, S. N. (2002): Methods of Computer Modeling in Engineering and Sciences, Tech. Science Press, 1400 pages.
2. Atluri, S. N.; Shen, S. (2002): The meshless local Petrov-Galerkin (MLPG) method: a simple & less-costly alternative to the finite element and boundary element methods. CMES: Computer Modeling in Engineering & Sciences, vol.3, pp. 11-51.
3. Atluri, S. N.; Liu, H. T.; Han, Z. D. (2006): Meshless local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems. CMES: Computer Modeling in Engineering & Sciences, vol.14, pp. 141-152
4. Dennis, J. E. (1971): On the convergence of Broyden's method for nonlinear systems of equations. A class of methods for solving nonlinear simultaneous equations. Math. Comp., vol.25, pp. 559-567.
5. Dennis, J. E.; More, J. J. (1974): A characterization of superlinear convergence and its application to quasi-Newton method. Math. Comp., vol.28, pp. 549-560.
6. Dennis, J. E.; More, J. J. (1977): Quasi-Newton methods, motivation and theory. SIAM Rev., vol.19, pp. 46-89.
7. Duffy, Daniel J. (2006), Finite Difference Methods in Financial Engineering, A Partial Differential Equation Approach, John Wiley & Sons Ltd.
8. Liu, C.-S. (2006), The Lie-group shooting method for nonlinear two-point bound ary value problems exhibiting multiple solutions. CMES: Computer Modeling in Engineering & Sciences, vol.13, pp. 149-163.
9. Liu, C.-S. (2008a): A Lie-group shooting method for simultaneously estimating the independent damping and stiffness coefficients. CMES: Computer Modeling in Engineering & Sciences, vol.27, pp. 137-149.
10. Liu, C.-S. (2008b): A time-marching algorithm for solving non-linear obstacle problems with the aid of an NCP-function. CMC: Computers, Materials & Continua, vol.8, pp. 53-65.
11. Liu, C.-S.; Atluri, S. N. (2008c): 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.
12. Liu, C.-S. (2008d): A fictitious time integration method for two-dimensional quasilinear elliptic boundary value problems. CMES: Computer Modeling in Engineering and Sciences, vol.33, pp. 179-198.
13. Liu, C.-S.; Atluri, S. N. (2008e): A fictitious time integration method (FTIM) for solving mixed complementarity problems with applications to non-linear optimization. CMES: Computer Modeling in Engineering & Sciences, vol.34, pp. 155-178.
14. Liu, C.-S. (2008f): A fictitious time integration method for solving the discretized inverse Sturm-Liouville problems, for specified eigenvalues, CMES: Computer Modeling in Engineering & Sciences vol.36, pp. 261-286.
15. Liu, C.-S. (2009a): A fictitious time integration method for solving m-point boundary value problems. CMES: Computer Modeling in Engineering & Sciences, vol.39, pp. 125-154.
16. Liu, C.-S.; Atluri, S. N. (2009b): A fictitious time integration method for the numerical solution of the Fredholm integral equation and for numerical differentiation of noisy data, and its relation to the filter theory. CMES: Computer Modeling in Engineering & Sciences, vol.41, pp. 243-261.
17. Spedicato, E.; Hunag, Z. (1997): Numerical experience with Newton-like methods for nonlinear algebraic systems. Computing, vol.58, pp. 69-89.
18. William H.; Teukolsky, Saul A.; Vetterling,William T.; Flannery, Brian P. (2007): Numerical Recipes, The Art of Scientific Computing, Cambridge University Press.
19. 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.