Second Order Differential Equations

Lindsay A. Skinner ()
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Lindsay A. Skinner: University of Wisconsin - Milwaukee, Department of Mathematical Sciences

Chapter Chapter 3 in Singular Perturbation Theory, 2011, pp 27-48 from Springer

Abstract: Abstract We begin this chapter with the classic singular perturbation problem 3.1 $$\varepsilon ^{\prime\prime} + a(x,\varepsilon)y^\prime + b(x,\varepsilon)y = c(x,\varepsilon)y,$$ where $$ a(x,\varepsilon)>0,$$ subject to the boundary conditions $$ y(0,\varepsilon)=\alpha(\varepsilon)\,\, \rm{and}\,\, y(1,\varepsilon)=\beta(\varepsilon) $$ . It will be assumed that $$ a(x,\varepsilon), \, b(x,\varepsilon), \, c(x,\varepsilon)\, \epsilon\, {\rm{C}^\infty}\, \left([0,1]\,\times\,[0,\varepsilon_o] \right)\,{\rm{and}}\, \alpha(\varepsilon),\,\beta(\varepsilon)\,\epsilon \, {\rm{C}^\infty} \, \left([0,\varepsilon_o]\right) \,\, {\rm{for\, some}\, \varepsilon_o >\, 0}.$$

Keywords: Asymptotic Form; Nonlinear Integral Equation; Perturbation Calculation; Nonlinear Generalization; Previous Exercise (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-9958-0_3

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DOI: 10.1007/978-1-4419-9958-0_3

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