On Nonlinear Singularly Perturbed Initial Value Problems
Copyright policy )On Nonlinear Singularly Perturbed Initial Value Problems
The author studies the singular perturbation initial value problem for the nonlinear system \(x'=f(x,y,t,\epsilon),\) \(\epsilon y'=g(x,y,t,\epsilon)\) on a bounded interval \([0,1]\) with smooth vector functions \(f\) and \(g\) of dimensions \(m\) and \(n\) respectively and with prescribed vector function \(x(0),y(0)\). Under givenhypothesis the author obtains a limiting solution \(\begin{pmatrix} x_0(t) \\ y_0(t) \end{pmatrix}\) for \(t>0\) which satisfies the reduced problem \(x'_0 = f(x_0,y_0,t,0)\), \(0=g(x_{01}y_0,t,0)\), \(x_0(0)=x(0)\). This paper develops insight and intuition based on several solvable model problems, and it relates a variety of literature scattered throughout asymptotic and numerical analysis, stability and control theory and specific topics in applied mathematical modeling.
Singular perturbations for ordinary differential equations, mathematical modeling, Singular perturbations, turning point theory, WKB methods for ordinary differential equations, Nonlinear ordinary differential equations and systems, Asymptotic expansions of solutions to ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations
Singular perturbations for ordinary differential equations, mathematical modeling, Singular perturbations, turning point theory, WKB methods for ordinary differential equations, Nonlinear ordinary differential equations and systems, Asymptotic expansions of solutions to ordinary differential equations, Numerical methods for initial value problems involving ordinary differential equations
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