ISSN:
1573-2878
Keywords:
Nonlinear boundary-value problems
;
elliptic integrals
;
Jacobian elliptic functions
;
singular-perturbation problems
;
matched asymptotic expansions
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In Ref. 1, the author claimed that the problem ∈y″=y 3 is soluble only for a certain range of the parameter ∈. An analytic approach, as adopted in the following contribution, reveals that a unique solution exists for any positive value of ∈. The solution is given in closed form by means of Jacobian elliptic functions, which can be numerically computed very efficiently. In the limit ∈→0+, the solutions exhibit boundary-layer behavior at both endpoints. An easily interpretable approximate solution for small ∈ is obtained using a three-variable approach.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02192942
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