Computed Eigenvalues

Perturbation Method

[22]

Rel. Error for Computed Eigenvalues

${\epsilon }_k=\left|\frac{{\lambda }^{Pert.}-{\lambda }^{\left(Gal.\right)}}{{\lambda }^{Pert.}}\right|<\delta$

Odd solutions

Even solutions

Error odd mode

Error even mode

e

n

${\lambda }_1^c$

${\lambda }_2^c$

${\lambda }_1^s$

${\lambda }_2^s$

${\lambda }_1^c$

${\lambda }_2^c$

${\lambda }_1^s$

${\lambda }_2^s$

0

${\pi }^2$

$4{\pi }^2$

${\pi }^2$

$4{\pi }^2$

${\pi }^2$

$4{\pi }^2$

${\pi }^2$

$4{\pi }^2$

0.1

12

10.3353264

39.34632940

9.34836591

39.34632938

2.072e-05

3.675e-06

1.188e-05

3.685e-06

0.2

20

10.7455317

38.94414302

8.77161090

38.94414302

2.427e-04

5.786e-05

2.670e-05

5.886e-05

0.3

20

11.1002207

38.25409317

8.13933938

38.25409321

1.002e-03

2.789e-04

1.509e-04

2.842e-04

0.4

20

11.3993931

37.24657106

7.45155132

37.24657104

2.856e-03

8.088e-04

2.842e-04

8.274e-04

0.5

20

11.6430489

35.88012433

6.70824674

35.88012433

6.669e-03

1.634e-03

1.079e-03

1.661e-03

0.6

20

11.8311883

34.10145713

5.90942563

34.10145715

1.397e-02

1.397e-02

1.170e-02

2.343e-03

0.7

20

11.9638111

31.84543005

5.05508800

31.84543017

2.721e-02

1.423e-03

3.056e-02

1.579e-03

0.8

20

12.0409174

29.03506020

4.14523385

29.03506020

5.190e-02

8.551e-03

7.774e-02

7.738e-03

0.9

20

12.0625071

25.58152113

3.17986316

25.58152112

1.031e-01

5.273e-02

2.105e-01

5.283e-02