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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 6, Pages 972–983 (Mi zvmmf10908)  

The least square method for systems of linear ordinary differential equations

A. A. Abramova, L. F. Yukhnob

a Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control," Russian Academy of Sciences, Moscow, 119333 Russia
b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia

Abstract: Some techniques for applying the least square method to solve boundary value problems for overdetermined systems of linear ordinary differential equations with redundant boundary conditions are considered. Problems of this type may have no solution in the general case. Within these techniques for the above problems, the variational approach is applied to both systems of equations and relevant boundary conditions. In one of these techniques, the order of equations of the system under consideration is increased; in this case, additional boundary conditions are set for it. Model examples of applying the techniques and their comparison are given.

Key words: overdetermined system of linear ordinary differential equations, boundary value problem, redundant boundary conditions, least square method.

DOI: https://doi.org/10.1134/S0044466919060024


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:6, 915–925

Bibliographic databases:

UDC: 519.624
Received: 09.01.2019
Revised: 09.01.2019
Accepted:08.02.2019

Citation: A. A. Abramov, L. F. Yukhno, “The least square method for systems of linear ordinary differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 59:6 (2019), 972–983; Comput. Math. Math. Phys., 59:6 (2019), 915–925

Citation in format AMSBIB
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