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Article information
2003 , Volume 8, ¹ 5, p.102-116
Rogalev A.N.
Guaranteed methods of ordinary differential equations solution on the basis of transformation of analytical formulas
We consider the systems of ordinary differential equations containing parameters which are not defined exactly, but specified in a certain interval. It is required to define a set of solutions which covers all solutions arising due to the variations of the parameters.The guaranteed method is based on the fact that the solution of a system can be expressed at any point as the analytical function depending on the initial data. Then the interval extension including all sets of solutions is constructed for this analytical function. These methods ensure the inclusions of sets of solutions of ODE systems in the obtained interval bounds.
[full text] Classificator Msc2000:- *34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
- 34B45 Boundary value problems on graphs and networks
Keywords: initial value problem, high-order interval method, interval analysis, numerical integration
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. Guaranteed methods of ordinary differential equations solution on the basis of transformation of analytical formulas // Computational technologies. 2003. V. 8. ¹ 5. P. 102-116
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