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Theory and Modern Applications

Table 1 The numerical results for the approximate solutions obtained by HPM [4] and HAM in comparison with the exact solutions of ( 3.1 )

From: Approximate analytic solutions of the modified Kawahara equation with homotopy analysis method

X

Time

HPM

HAM

Exact solution

−0.5

0.02

9.474889415e − 4

9.474889415e − 4

9.474889415e − 4

−2.5

0.04

9.483868961e − 4

9.483868961e − 4

9.483773375e − 4

0.0

0.06

9.486832980e − 4

9.486832980e − 4

9.486831272e − 4

2.5

0.08

9.483868961e − 4

9.483868961e − 4

9.484055589e − 4

5.0

1.0

9.474984315e − 4

9.474984315e − 4

9.475453144e − 4