Bulirsch
R.
1994-02
means
article
https://doi.org/10.1007/bf02192942
analytic approach
parameters
range
solution
limit
approximate solution
certain range
form
false
2022-08-04T16:50
367-372
In Ref. 1, the author claimed that the problem ∈y″=y3 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.
approach
Jacobian elliptic functions
Ref. 1
closed form
On the complete solution of ∈y″=y3
elliptic functions
positive values
complete solution
1994-02-01
endpoint
values
authors
behavior
articles
contribution
problem
boundary layer behavior
https://scigraph.springernature.com/explorer/license/
unique solution
function
Department of Mathematics, University of Technology, Munich, Germany
Department of Mathematics, University of Technology, Munich, Germany
80
K. -D.
Reinsch
2
Springer Nature - SN SciGraph project
1573-2878
Springer Nature
0022-3239
Journal of Optimization Theory and Applications
dimensions_id
pub.1010726532
Pure Mathematics
Müller
P. N.
doi
10.1007/bf02192942
Mathematical Sciences