Table 1 Comparative study between ATHPM [61], LTDM [50], and q-HSATM for the numerical solutions \({u} ( {x}, {t} )\) at \({\alpha} ={1}\) and \({\beta} ={0}.{01}\)
From: A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation
t | \(\vert {u}_{{exact}} - {u}_{{ATHPM}} \vert \) | \(\vert {u}_{{exact}} - {u}_{{LTDM}} \vert \) | \(\vert {u}_{{exact}} - {u}_{{q}-{HSATM}} \vert \) |
|---|---|---|---|
0.001 | 1 × 10−12 | 7.56 × 10−7 | 1 × 10−12 |
0.002 | 9 × 10−11 | 1.51 × 10−6 | 9 × 10−11 |
0.003 | 3.2 × 10−10 | 2.26 × 10−6 | 3.2 × 10−10 |
0.004 | 7.7 × 10−10 | 3.02 × 10−6 | 7.7 × 10−10 |
0.005 | 1.5 × 10−9 | 3.78 × 10−6 | 1.5 × 10−9 |
0.006 | 2.6 × 10−9 | 4.53 × 10−6 | 2.6 × 10−9 |
0.007 | 4.1 × 10−9 | 5.20 × 10−6 | 4.1 × 10−9 |
0.008 | 6.1 × 10−9 | 6.00 × 10−6 | 6.1 × 10−9 |
0.009 | 8.7 × 10−9 | 6.80 × 10−9 | 8.7 × 10−9 |
0.010 | 1.2 × 10−8 | 7.05 × 10−6 | 1.2 × 10−8 |