Table 2 Shows analysis of Perturb solution with numerical solution for stream function with \(\alpha = 0.2, \varepsilon = 0.15, \delta =0.01, F= 0.1, x= 1\).

From: A novel mathematical modeling with solution for movement of fluid through ciliary caused metachronal waves in a channel

y

Perturb solution

Numerical solution

Difference

0.

0.

0.

0.

0.1

0.0560456

0.0560623

\(-\,1.67013\times 10^{\text {-5}}\)

0.2

0.109734

0.109766

\(-\,3.20222\times 10^{\text {-5}}\)

0.3

0.158706

0.15875

\(-\,4.45712\times 10^{\text {-5}}\)

0.4

0.200601

0.200655

\(-\,5.31095\times 10^{\text {-5}}\)

0.5

0.233058

0.233115

\(-\,5.67039\times 10^{\text {-5}}\)

0.6

0.25371

0.253765

\(-\,5.49514\times 10^{\text {-5}}\)

0.7

0.260185

0.260233

\(-\,4.81658\times 10^{\text {-5}}\)

0.8

0.250107

0.250144

\(-\,3.74213\times 10^{\text {-5}}\)

0.9

0.221092

0.221116

\(-\,2.44263\times 10^{\text {-5}}\)

1.

0.17075

0.170762

\(-\,1.14196\times 10^{\text {-5}}\)

1.1

0.0966832

0.0966849

\(-\,1.73212\times 10^{\text {-6}}\)