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Theory and Modern Applications

Table 2 The \(L_{\infty }\) norm error with \(\tau = 0.0025\) at \(t = 1\) for different h for Problem 1

From: An explicit fourth-order compact difference scheme for solving the 2D wave equation

h

THOC-ADI [5]

HOC-LOD [5]

CPD-ADI [5]

IPD-ADI [5]

EFOC scheme

1/5

1.3769(−6)

1.3757(−6)

1.3769(−6)

1.3769(−6)

1.3416(−6)

1/10

8.6606(−8)

8.6343(−8)

8.6608(−8)

2.0245(−8)

8.5804(−8)

1/20

5.4688(−9)

5.4730(−9)

5.4690(−9)

1.4498(−9)

5.4069(−9)

1/40

3.4449(−10)

3.7600(−10)

3.4277(−10)

1.0746(−10)

3.3029(−10)

1/80

2.5746(−11)

3.4394(−11)

2.3074(−11)

5.4340(−12)

1.9000(−11)