A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics

International Journal for Numerical Methods in Engineering

Volumn 61, Issue 5, 2004, Pages 764-790

  Roy, D ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Additive and multiplicative noises; Engineering systems; Higher order schemes; Ito Taylor expansions; Local and global error orders; Transversal linearization

Indexed keywords

ERROR ANALYSIS; NUMERICAL METHODS; PROBLEM SOLVING; STOCHASTIC CONTROL SYSTEMS; VECTORS; WHITE NOISE;

LOCALLY TRANSVERSAL LINEARIZATION (LTL); WHITE NOISE EXCITATIONS;

SYSTEMS ENGINEERING;

DYNAMICAL SYSTEM;

EID: 4544231659     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1089     Document Type: Article

References (12)

1. Gillespie DT. Markov Processes: An Introduction for Physical Scientists. Academic Press Inc: San Diego, CA, 1992.
2. Gard TC. Introduction to Stochastic Differential Equations. Marcel Dekker Inc: New York, 1988.
3. Kloeden PE, Platen E. Numerical Solution of Stochastic Differential Equations. Springer: Berlin, 1999.
4. Maruyama G. Continuous Markov processes and stochastic equations. Rendiconti del Circolo Matematica di Palermo 1955; 4:48-90.
5. Gikhman II, Skorokhod AV. Stochastic Differential Equations. Springer: Berlin, 1972.
6. Kanagawa S. Confidence intervals of discretized Euler-Maruyama approximate solutions of SDEs. Nonlinear Analysis 1997; 30:4101-4104.
7. Wagner W, Platen E. Approximation of Ito integral equations. Preprint, ZIMM, Akad. Wissenschaften, DDR, Berlin, 1978.
8. Milstein GN. Numerical Integration of Stochastic Differential Equations. Kluwer Academic Publishers: Dordrecht, 1995.
9. Kloeden PE, Platen E. Higher order implicit strong numerical schemes for stochastic differential equations. Journal of Statistical Physics 1992; 66:283-314.
10. Rumelin W. Numerical treatment of stochastic differential equations. SIAM Journal on Numerical Analysis 1982; 19:604-613.
11. Roy D. A new numeric-analytic principle for non-linear deterministic and stochastic dynamical systems. Proceedings of the Royal Society of London A 2001; 457:539-566.
12. Leung AYT. Fast matrix exponent for deterministic or random excitations. International Journal for Numerical Methods in Engineering 2001; 50:377-394.