Table 2 Comparison between the least squares residual power series method (LSRPSM) and the residual power series method (RPSM) for problem 2 at \(\:\alpha\:=1\).

From: Least squares residual power series solutions for Kawahara and Rosenau-Hyman nonlinear wave interactions with applications in fluid dynamics

t

x

LSRPS

Exact

Absolute error (LSRPSM)

Absolute error (RPSM)18

0

10

0.030421

0.030421

0

0

0.1

0.030739

0.030739

6.7233E − 16

1.41553E − 15

0.2

0.031061

0.031061

9.124E − 15

4.68063E − 14

0.3

0.031386

0.031386

9.9486E − 14

3.6391E − 13

0.4

0.031714

0.031714

5.4738E − 13

1.56886E − 12

0.5

0.032046

0.032046

2.0665E − 12

4.89617E − 12

0.6

0.03238

0.03238

6.0629E − 12

1.24542E − 11

0.7

0.032718

0.032718

1.4917E − 11

2.75069E − 11

0.8

0.033059

0.033059

3.2291E − 11

5.47829E − 11

0.9

0.033403

0.033403

6.3467E − 11

1.0081E − 10

1

0.033715

0.033715

1.1571E − 10

1.7428E − 10