The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations

Huang Wei-zhang

Volume 13 Issue 8

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Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(8): 719-727

Huang Wei-zhang. The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations[J]. Applied Mathematics and Mechanics, 1992, 13(8): 719-727.

Citation:

Huang Wei-zhang. The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations[J]. Applied Mathematics and Mechanics, 1992, 13(8): 719-727.

Citation:

Huang Wei-zhang. The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations[J]. Applied Mathematics and Mechanics, 1992, 13(8): 719-727.

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The Estimation of Solution of the Boundary Value Problem of the Systems for Quasi-Linear Ordinary Differential Equations

Huang Wei-zhang

Fuqing Branch Campus of Fujian Normal University, Fuqing, Fujian

Received Date: 1991-07-17
Publish Date: 1992-08-15

Abstract

Abstract

This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equations x'=f(t,x,y,ε),x(0,ε)=A(ε) εy"=g(t,x,y,ε)y'+h(t,x,y,ε) y(0,ε)=B(ε),y(1,ε)=C(ε) where x,f, y, h, A, B and C all belong to Rⁿ, and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.
- systems of the quasi-linear ordinary differential equation,
- singular perturbation,
- diagonalization,
- asymptotic expansion

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References(6)

References

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[3]	Smith, D. R.,Singular Perturbation Theory, An Introduction with Applications, Cambridge University Press, Cambridge (1985).
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