Reduction from a Semi-Infinite Interval to a Finite Interval of a Nonlinear Boundary Value Problem for a System of Second-Order Equations with a Small Parameter
- A. I. Zadorin
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We consider a boundary value problem over a semi-infinite interval for a nonlinear autonomous system of second-order ordinary differential equations with a small parameter at the leading derivatives. We impose certain constraints on the Jacobian under which a solution to the problem exists and is unique. To transfer the boundary condition from infinity, we use the well-known approach that rests on distinguishing the variety of solutions satisfying the limit condition at infinity. To solve an auxiliary Cauchy problem, we apply expansions of a solution in the parameter.
- Voevodin, V. V., Kuznetsov, Y. A. (1984) Matrices and Calculations. Nauka, Moscow
- Konyukhova, N. B., Pak, T. V. (1987) Transfer of admissible boundary conditions at infinity for systems of linear ordinary differential equations with a large parameter. Zh. Vychisl. Mat. i Mat. Fiz. 27: pp. 847-866
- Abramov A. A., Balla K., and Konyukhova N. B., “Transfer of boundary conditions from singular points for systems of ordinary differential equations,” in: Soobshch. po Vychisl. Matematike, Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1981.
- Konyukhova N. B., “Smooth Lyapunov manifolds and singular boundary problems,” in: Soobshch. po Vychisl. Matematike, Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1996.
- Zadorin, A. I. (1998) Numerical solution of an equation with a small parameter on an infinite interval. Zh. Vychisl. Mat. i Mat. Fiz. 38: pp. 1671-1682
- Zadorin, A. I. (1999) Transferring a boundary condition from infinity in the case of numeric solution to second-order linear equations with a small parameter. Sibirsk. Zh. Vychisl. Mat. 2: pp. 21-35
- Konyukhova, N. B., Pak, T. V. (1987) Singular Cauchy problems with a large parameter for systems of nonlinear ordinary differential equations. Zh. Vychisl. Mat. i Mat. Fiz. 27: pp. 501-519
- Konyukhova, N. B. (1994) A stationary Lyapunov problem for a system of first-order quasilinear partial differential equations. Differentsial'nye Uravneniya 30: pp. 1384-1395
- Coddington E. A. and Levinson N., Theory of Ordinary Differential Equations [Russian translation], Izdat. Inostr. Lit., Moscow (1958).
- Reduction from a Semi-Infinite Interval to a Finite Interval of a Nonlinear Boundary Value Problem for a System of Second-Order Equations with a Small Parameter
Siberian Mathematical Journal
Volume 42, Issue 5 , pp 884-892
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- A. I. Zadorin (1)
- Author Affiliations
- 1. The Institute of Applied Mathematics of the Far East Division of the, Russian Academy of Sciences, Khabarovsk