Theory and Modern Applications
Table 4 The \(L_{\infty }\) and \(L_{2}\) norm errors with \(\tau =0.0002\) at \(t=0.02\) for different h for Problem 2
From: An explicit fourth-order compact difference scheme for solving the 2D wave equation
h | New LOD scheme [34] | Typical 4th-order scheme [34] | EFOC scheme | |||
|---|---|---|---|---|---|---|
\(L_{2}\)-error | \(L_{\infty }\)-error | \(L_{2}\)-error | \(L_{\infty }\)-error | \(L_{2}\)-error | \(L_{\infty }\)-error | |
1/10 | 1.75(−6) | 3.85(−6) | 2.32(−6) | 1.02(−5) | 7.95(−8) | 1.59(−7) |
1/20 | 1.14(−7) | 2.40(−7) | 2.74(−7) | 6.38(−7) | 4.95(−9) | 9.91(−9) |
1/40 | 7.31(−9) | 1.50(−8) | 1.91(−8) | 3.99(−8) | 3.09(−10) | 6.19(−10) |
1/80 | 4.62(−10) | 9.36(−10) | 1.23(−9) | 2.50(−9) | 1.93(−11) | 3.86(−11) |
1/160 | 2.91(−11) | 5.85(−11) | 7.75(−11) | 1.57(−10) | 1.20(−12) | 2.42(−12) |
1/320 | 2.38(−12) | 4.79(−12) | 4.99(−12) | 1.39(−11) | 7.48(−14) | 1.65(−13) |