Table 5 The numerical solutions and the absolute errors of Problem 5.2 for \(t=3\), \(\alpha =1\), \(s=0.1\), \(\mu =0.3\), \(\gamma =0.4 \), and \(\xi =0.8\)
From: Parametric quintic spline for time fractional Burger’s and coupled Burgers’ equations
x | Exact solution | PQSM | CPS [3] | Absolute errors of | |
|---|---|---|---|---|---|
PQSM | CPS [3] | ||||
−1.80 | 0.6999932828 | 0.69999336 | 0.69999302 | 7.614 × 10−8 | 2.608 × 10−7 |
−1.50 | 0.6999834786 | 0.69998367 | 0.69998276 | 1.938 × 10−7 | 7.193 × 10−7 |
−0.96 | 0.6999165251 | 0.69991749 | 0.69991259 | 9.657 × 10−7 | 3.931 × 10−6 |
−0.48 | 0.6989641713 | 0.69897337 | 0.69963109 | 9.198 × 10−6 | 6.669 × 10−4 |
0.00 | 0.6985164261 | 0.69852846 | 0.69844644 | 1.203 × 10−5 | 6.998 × 10−5 |
0.48 | 0.6937877575 | 0.69381151 | 0.69349918 | 2.375 × 10−5 | 2.886 × 10−4 |
0.96 | 0.6746261369 | 0.67458239 | 0.67349066 | 4.375 × 10−5 | 1.135 × 10−3 |
1.50 | 0.5905446857 | 0.58997244 | 0.58651442 | 5.722 × 10−4 | 4.030 × 10−3 |
1.80 | 0.4873937837 | 0.48661686 | 0.48167270 | 7.769 × 10−4 | 5.721 × 10−3 |