| Citation: |
Xinyu Wang, Na Wang. A CLASS OF HIGHER ORDER TURNING POINT NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 657-690. doi: 10.11948/20240002
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A CLASS OF HIGHER ORDER TURNING POINT NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM
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Abstract
When a boundary layer occurs close to a turning point in a class of singularly perturbation problems with turning points, the solution manifests as a multi-layer phenomena. This paper provides a systematic solution. It focuses on a class of turning point problems and the aspects include constructing formal asymptotic solutions. It also involves establishing the existence and error estimation of the solutions, the relationship with the position of the intermediate layer and boundary layer. In addition, the numerical verification is conducted as well.
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References
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Xinyu Wang, Na Wang. A CLASS OF HIGHER ORDER TURNING POINT NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM[J]. Journal of Applied Analysis & Computation, 2025, 15(2): 657-690. doi: 10.11948/20240002
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Figure 1.
The analysis figure of multilayer phenomenon when
$ k = 0, \varepsilon = 0.01 $ -
Figure 2.
Comparison of asymptotic and the numerical solutions when
$ k = 0, \varepsilon = 0.01 $ -
Figure 3.
Comparison of asymptotic and the numerical solutions when
$ k = 0, \varepsilon = 0.001 $ -
Figure 4.
Comparison of asymptotic and the numerical solutions when
$ k = 1, \varepsilon = 0.01 $ -
Figure 5.
Comparison of asymptotic and the numerical solutions when
$ k = 1, \varepsilon = 0.001 $ -
Figure 6.
Comparison of asymptotic and the numerical solutions when
$ k = 0.25, \varepsilon = 0.001 $ -
Figure 7.
Comparison plot with and without boundary layer terms when
$ k = 0.25, \varepsilon = 0.001 $ -
Figure 8.
Comparison of asymptotic and the numerical solutions when
$ k = 0.5, \varepsilon = 0.001 $ -
Figure 9.
Comparison of asymptotic and the numerical solutions when nonlinear and
$ k = 0, \varepsilon = 0.01 $ -
Figure 10.
Comparison of asymptotic and the numerical solutions when nonlinear and
$ k = 1, \varepsilon = 0.01 $ -
Figure 11.
Comparison of asymptotic and the numerical solutions when nonlinear and
$ k = 0.5, \varepsilon = 0.001 $ -
Figure 12.
Comparison plot with and without boundary layer terms when nonlinear and
$ k = 0.5, \varepsilon = 0.001 $