Singular perturbation of nonlinear vector boundary value problem
The authors consider the singularly perturbed boundary value problem for a system of nonlinear vector ordinary differential equations of the form \[ dx/dt=f(x,y,t;\epsilon),\quad \epsilon dy/dt=g(x,y,t;\epsilon), \] \[ a_ 1(\epsilon)x(0,\epsilon)+a_ 2(\epsilon)y(0,\epsilon)=\alpha (\epsilon),\quad b_ 1(\epsilon)x(1,\epsilon)+\epsilon b_ 2(\epsilon)y(1,\epsilon)=\beta (\epsilon). \] The asymptotic expansion of the solution is constructed, the remainder term is estimated. The work of \textit{F. Hoppensteadt} [Commun. Pure Appl. Math. 24, 807-840 (1971; Zbl 0235.34120)] for initial value problem is generalized to the boundary value problems.
nonlinear vector ordinary differential equations
scientific article; zbMATH DE number 4208530