Numerical solution of stiff systems from nonlinear dynamics using single-term Haar wavelet series

Nonlinear Dynamics

Volumn 51, Issue 4, 2008, Pages 595-605

  Bujurke, N M ^a   Salimath, C S ^a   Shiralashetti, S C ^b  

^a KARNATAK UNIVERSITY   (India)

^b SDM COLLEGE OF ENGINEERING AND TECHNOLOGY   (India)

Author keywords

Block pulse and discrete solutions; Fluid dynamics; Gill's method; Nonlinear stiff systems; Operational matrix; STHWS

Indexed keywords

FLUID DYNAMICS; NUMERICAL METHODS; PROBLEM SOLVING; STIFFNESS; WAVELET ANALYSIS;

DISCRETE SOLUTIONS; GILL METHOD; OPERATIONAL MATRIX;

NONLINEAR SYSTEMS;

EID: 38349094162     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-007-9248-8     Document Type: Article

References (19)

1. Steinfield, J.I., Fransisco, J.S., Hase, W.L.: Chemical Kinetics and Dynamics. Prentice-Hall, Englewood Cliffs, NJ (1999)
2. Carrol, J.: A matricial exponentially fitted scheme for the numerical solution of stiff initial value problems. Comput. Math. Appl. 26, 57-64 (1993)
3. Pavlov, B.V., Rodionova, O.E.: Numerical solution of systems of linear ordinary differential equations with constant coefficients. Comput. Math. Phys. 34, 535-539 (1994)
4. Hsiao, C.H.: Haar wavelet approach to linear stiff systems. Math. Comput. Simul. 64, 561-567 (2004)
5. Chen, C.F., Hsiao, C.H.: Haar wavelet method for solving lumped and distributed parameter systems. IEE Proc. Control Theory Appl. 144(1), 87-94 (1997)
6. Rao, G.P., Palanisamy, K.R., Srinivasan, T.: Extension of computation beyond the limit of initial normal interval in Walsh series analysis of dynamical systems. IEEE Trans. Autom. Control 25, 317-319 (1980)
7. Balachandran, K., Muragesan, K.: Analysis of different systems via single-term Walsh series method. Int. J. Comput. Math. 33, 171-179 (1990)
8. Sepehrian, B., Razzaghi, M.: Solution of time-varying singular nonlinear systems by single-term Walsh series. Math. Prob. Eng. 3, 129-136 (2003)
9. Shampine, L.F., Hosea, M.E.: Analysis and implementation of TR-BDF2. Appl. Numer. Math. 20, 21-37 (1996)
10. Wojtaszezyk, P.: A Mathematical Introduction to Wavelets. Cambridge University Press, Cambridge, U.K. (1997)
11. Sannuti, P.: Analysis and synthesis of dynamical systems via block-pulse functions. Proc. IEE 124, 569-571 (1977)
12. Brown, K.M.: Solution of simultaneous nonlinear equations. Commun. ACM 10, 728-729 (1967)
13. Finlayson, B.A.: Nonlinear Analysis in Chemical Engineering. McGraw Hill, New York (1980)
14. Hindmarsh, A.C., Byrne, G.D.: EPISODE: an effective pakage for the integration of systems of ordinary differential equations. Report UCID-30112, Rev. 1, Lawrence Livermore Laboratory, Livermore, CA (April 1977)
15. Shampine, L.F., Gear, C.W.: A user's view of solving stiff ordinary differential equations. SIAM Rev. 21, 1-17 (1979)
16. Byrne, G.D., Hindmash, A.C.: Numerical Solution of Stiff Ordinary Differential Equations, AIChE Today Series. American Institute of Chemical Engineers, New York (1977)
17. Scraton, R.E.: Further Numerical Methods in Basic. Arnold, London (1987)
18. Neil, C.H.: Existence, uniqueness and behavior of solutions of a singular nonlinear system from fluid dynamics. SIAM J. Appl. Math. 44, 512-523 (1984)
19. Watkins, D.S.: Determining initial values for stiff systems of ordinary differential equations. SIAM J. Numer. Anal. 18(1), 13-20 (1981)