Table 4 \(C_{2}\)-order of convergence for Test problem 3
γ = 0.1 | ||
|---|---|---|
h/τ | Max error | \(C_{2}\)-order |
\(h =\tau =\frac{1}{2}\) | 9.293 × 10−2 | – |
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\) | 6.869 × 10−3 | 3.76 |
\(h = \tau =\frac{1}{4}\) | 4.962 × 10−2 | – |
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\) | 3.558 × 10−3 | 3.80 |
γ = 0.2 | ||
|---|---|---|
h/τ | Max error | \(C_{2}\)-order |
\(h =\tau =\frac{1}{2}\) | 8.200 × 10−2 | – |
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\) | 5.916 × 10−3 | 3.78 |
\(h = \tau =\frac{1}{4}\) | 4.298 × 10−2 | – |
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\) | 3.058 × 10−3 | 3.81 |
γ = 0.3 | ||
|---|---|---|
h/τ | Max error | \(C_{2}\)-order |
\(h =\tau =\frac{1}{2}\) | 7.092 × 10−2 | – |
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\) | 5.068 × 10−3 | 3.81 |
\(h = \tau =\frac{1}{4}\) | 3.643 × 10−2 | – |
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\) | 2.616 × 10−3 | 3.80 |
γ = 0.4 | ||
|---|---|---|
h/τ | Max error | \(C_{2}\)-order |
\(h =\tau =\frac{1}{2}\) | 5.966 × 10−2 | — |
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\) | 4.206 × 10−3 | 3.83 |
\(h = \tau =\frac{1}{4}\) | 2.996 × 10−2 | — |
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\) | 2.171 × 10−4 | 3.80 |
γ = 0.5 | ||
|---|---|---|
h/τ | Max error | \(C_{2}\)-order |
\(h =\tau =\frac{1}{2}\) | 4.824 × 10−2 | – |
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\) | 3.402 × 10−3 | 3.82 |
\(h = \tau =\frac{1}{4}\) | 2.359 × 10−2 | – |
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\) | 1.669 × 10−3 | 3.82 |
γ = 0.6 | ||
|---|---|---|
h/τ | Max error | \(C_{2}\)-order |
\(h =\tau =\frac{1}{2}\) | 3.668 × 10−2 | – |
\(h =\frac{1}{4} \), \(\tau =\frac{1}{32}\) | 2.652 × 10−3 | 3.79 |
\(h = \tau =\frac{1}{4}\) | 1.735 × 10−2 | – |
\(h =\frac{1}{8} \), \(\tau =\frac{1}{64}\) | 1.201 × 10−3 | 3.85 |