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Article information
2003 , Volume 8, ¹ 6, p.80-94
Rogalev A.N.
Inclusion of sets of solutions of the differential equations and guaranteed estimations of global errors
An inclusion of solutions and global error estimation are proved for the guaranteed methods, based on approximations of the shift operator along a trajectory and conversion of the analytical formulas of solutions. Algorithms of evaluation of numerical values of guaranteed bounds are considered. The convergence of guaranteed boundaries to a set of exact solutions, considered in projections to coordinate axes, is proved.
[full text] Classificator Msc2000:- *34A09 Implicit equations, differential-algebraic equations
- 65G40 General methods in interval analysis
- 65L70 Error bounds
- 65L80 Methods for differential-algebraic equations
Classificator Computer Science:- *G.1.0 General (Numerical Analysis)
- G.1.7 Ordinary Differential Equations
Keywords: interval method, differential algebraic method, inclusion of solutions, global error estimation, algorithms, convergence
Author(s):
Rogalev Alexey Nikolaevich
PhD. , Associate Professor
Position: Associate Professor
Office: Institute of Computational Modelling SB RAS
Address: 660036, Russia, Krasnoyarsk, Akademgorodok, 50, p.44
E-mail: rogalyov@icm.krasn.ru
SPIN-code: 7519-8826
Bibliography link:
Rogalev A.N. Inclusion of sets of solutions of the differential equations and guaranteed estimations of global errors // Computational technologies. 2003. V. 8. ¹ 6. P. 80-94
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