Theory and Modern Applications
Table 1 The spacial error and convergence order of the scheme for different γ, α, β with \(\tau=1/1000\)
γ = 1.7, α = 0.8, β = 0.6 | \(L_{2} \) error | Order | \(L_{\infty}\) error | Order |
|---|---|---|---|---|
h = 1/4 | 3.5954E−02 | 7.1908E−02 | ||
h = 1/8 | 8.8281E−03 | 2.03 | 1.7656E−02 | 2.03 |
h = 1/16 | 2.1957E−03 | 2.01 | 4.3914E−03 | 2.01 |
h = 1/32 | 5.4676E−04 | 2.01 | 1.0935E−03 | 2.01 |
h = 1/64 | 1.3510E−04 | 2.02 | 2.7020E−04 | 2.02 |
γ = 1.5, α = 0.6, β = 0.4 | \(L_{2} \) error | Order | \(L_{\infty}\) error | Order |
|---|---|---|---|---|
h = 1/4 | 3.5339E−02 | 7.0678E−02 | ||
h = 1/8 | 8.6774E−03 | 2.03 | 1.7355E−02 | 2.03 |
h = 1/16 | 2.1590E−03 | 2.01 | 4.3181E−03 | 2.01 |
h = 1/32 | 5.3849E−04 | 2.00 | 1.0770E−03 | 2.00 |
h = 1/64 | 1.3392E−04 | 2.01 | 2.6784E−04 | 2.01 |
γ = 1.2, α = 0.4, β = 0.2 | \(L_{2} \) error | Order | \(L_{\infty}\) error | Order |
|---|---|---|---|---|
h = 1/4 | 3.4841E−02 | 6.9682E−02 | ||
h = 1/8 | 7.7561E−03 | 2.03 | 1.7108E−02 | 2.03 |
h = 1/16 | 1.9248E−03 | 2.01 | 4.2575E−03 | 2.01 |
h = 1/32 | 4.7517E−04 | 2.02 | 1.0628E−03 | 2.00 |
h = 1/64 | 1.1326E−04 | 2.00 | 2.6526E−04 | 2.00 |