Table 1 The absolute errors of problem (30) for our method at \(N=8\) and the NSFD method in Sweilam and Assiri (2015)
From: A space–time spectral collocation algorithm for the variable order fractional wave equation
x | t | Our method | NSFD method (Sweilam and Assiri 2015) | ||
|---|---|---|---|---|---|
\(\theta _{1}=\theta _{2}=0\) | \(\theta _{1}=\theta _{2}=\frac{1}{2}\) | \(\theta _{1}=1,\theta _{2}=0\) | \(N=1000\) | ||
\(\vartheta _{1}=\vartheta _{2}=0\) | \(\vartheta _{1}=\vartheta _{2}=\frac{1}{2}\) | \(\vartheta _{1}=0,\vartheta _{2}=1\) | \(M=125\) | ||
0 | 1 | 2.15204 × 10−14 | 3.55271 × 10−14 | 0 | 0 |
0.8 | 2.1985 × 10−15 | 9.9476 × 10−14 | 3.55271 × 10−14 | 2.70905 × 10−3 | |
1.6 | 1.22734 × 10−14 | 1.84741 × 10−13 | 1.42109 × 10−14 | 2.47795 × 10−3 | |
2.4 | 1.60228 × 10−14 | 5.68434 × 10−14 | 7.10543 × 10−14 | 2.12119 × 10−3 | |
3.2 | 3.54371 × 10−15 | 1.42109 × 10−14 | 1.42109 × 10−14 | 1.62219 × 10−3 | |
4 | 1.69769 × 10−14 | 2.84217 × 10−14 | 2.84217 × 10−14 | 9.1329 × 10−4 | |
4.8 | 1.93105 × 10−14 | 8.52651 × 10−14 | 5.68434 × 10−14 | 9.988 × 10−5 | |
5.6 | 5.34145 × 10−14 | 0 | 0 | 1.52948 × 10−3 | |
6.4 | 2.16945 × 10−14 | 1.42109 × 10−14 | 2.13163 × 10−14 | 3.50169 × 10−3 | |
7.2 | 5.49134 × 10−14 | 3.55271 × 10-15 | 0 | 6.15396 × 10−3 | |
8 | 1.37362 × 10−15 | 1.42109 × 10−14 | 0 | 0 | |