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Solving a system of linear ordinary differential equations with redundant conditions |
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| Authors: | A. A. Abramov L. F. Yukhno |
| Affiliation: | 1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia 3. Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia (MFTI) 2. Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4a, Moscow, 125047, Russia 4. Moscow Engineering Physics Institute (State University), Kashirskoe sh. 31, Moscow, 115409, Russia (MIFI) |
| Abstract: | A system of linear ordinary differential equations is examined under the assumption that, in addition to the basic conditions, which in general are nonlocal and are specified by a Stieltjes integral, certain redundant (and possibly also nonlocal) conditions are imposed. Generically, such a problem has no solution. A principle for constructing an auxiliary system is proposed. This system replaces the original one and is normally consistent with all the conditions prescribed. A method for solving this auxiliary problem is analyzed. The method is numerically stable if the auxiliary problem is numerically stable. |
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