Table 2: The comparison of the results of the HAM ( = 1 ) and exact solution for the 𝑢 ( 𝑥 , 𝑡 ) , 𝛼 = 𝛽 = 1 .

x t | 5 𝑖 = 0 𝑢 ( 𝑖 ) E x a c t | | 5 𝑖 = 0 𝑣 ( 𝑖 ) E x a c t |

−15 0.002 8 . 0 6 7 2 × 1 0 8 2 . 4 4 2 6 × 1 0 8
−12 0.002 5 . 9 5 3 9 × 1 0 7 1 . 8 0 3 8 × 1 0 7
−6 0.002 3 . 0 2 5 7 × 1 0 6 1 . 3 2 7 0 × 1 0 6
6 0.002 3 . 0 2 6 3 × 1 0 6 1 . 3 4 8 1 × 1 0 6
12 0.002 5 . 9 5 5 0 × 1 0 7 1 . 7 7 2 2 × 1 0 7
15 0.002 8 . 0 6 8 6 × 1 0 8 2 . 3 9 9 8 × 1 0 8