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

x t 𝜙 6 u( 𝑥 , 𝑡 ) Realtive error

10 0.01 −5.3861e-001 −0.9002497662 4 . 5 2 5 3 𝑒 × 1 0 1 3
10 0.02 −5.3325e-001 −0.8912921314 1 . 4 4 5 9 × 1 0 1 1
10 0.03 −5.2794e-001 −0.8824236265 1 . 0 9 6 2 × 1 0 1 0
5 0.01 −0.9493828183 −0.9493828187 7 . 9 7 8 1 × 1 0 1 3
5 0.02 −0.9399363019 −0.9399363019 2 . 5 4 8 6 × 1 0 1 1
5 0.03 −0.9305837792 −0.9305837793 1 . 9 3 2 2 × 1 0 1 0
-2 0.01 −0.5386080102 −0.5386080104 7 . 5 6 5 1 × 1 0 1 3
-2 0.02 −0.5332487712 −0.5332487712 2 . 4 1 6 7 × 1 0 1 1
-2 0.03 −0.5279428571 −0.5279428572 1 . 8 3 2 2 × 1 0 1 0