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Theory and Modern Applications

Table 3 Errors of different sixth-order schemes \((k=10)\)

From: Sixth-order finite difference scheme for the Helmholtz equation with inhomogeneous Robin boundary condition

N

20

40

80

160

EB

5.47e − 006

8.36e − 008

1.30e − 009

2.00e − 011

EB6

4.44e − 005

2.03e − 007

1.31e − 009

1.94e − 011

FLAME

4.64e − 005

2.33e − 007

1.67e − 009

1.97e − 011

HO (Γ = 0)

1.85e − 005

2.83e − 007

4.38e − 009

6.85e − 011

QSFEM

4.62e − 005

2.29e − 007

1.62e − 009

1.93e − 011

QOFD

4.62e − 005

2.29e − 007

1.62e − 009

1.93e − 011

QOFDT6

8.52e − 004

1.41e − 005

2.24e − 007

3.50e − 009

T4QOFD

7.78e − 004

1.28e − 005

2.03e − 007

3.17e − 009

T6QOFD

4.23e − 005

2.13e − 007

1.57e − 009

1.93e − 011