Table 2 Comparison of localized solution with approximate solution for \(\mu _0=1\),and \(\bar{\tau }=0.01\).

From: Electron-acoustic solitary potential in nonextensive streaming plasma

\(\bar{\xi }\)

\(\bar{\zeta }\)=\(\bar{\xi }-\mu _0\bar{\tau }\)

Localized solution

MDLDM Solution

Absolute Error

− 3.0

− 3.01

− 5.5001\(\times 10^{-13}\)

− 5.971\(\times 10^{-13}\)

4.7095\(\times 10^{-14}\)

− 2.5

− 2.51

− 7.6063\(\times 10^{-11}\)

− 8.3828\(\times 10^{-11}\)

7.7646\(\times 10^{-12}\)

− 2.0

− 2.01

− 1.0519\(\times 10^{-08}\)

− 1.1608\(\times 10^{-08}\)

1.0885\(\times 10^{-09}\)

− 1.5

− 1.51

− 1.4547\(\times 10^{-06}\)

− 1.6054\(\times 10^{-06}\)

1.5071\(\times 10^{-07}\)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

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\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

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1.5

1.49

− 1.7718\(\times 10^{-06}\)

− 1.6055\(\times 10^{-06}\)

1.6633\(\times 10^{-07}\)

2.0

1.99

− 1.2812\(\times 10^{-08}\)

− 1.161\(\times 10^{-08}\)

1.2014\(\times 10^{-09}\)

2.5

2.49

− 9.2641\(\times 10^{-11}\)

− 8.406\(\times 10^{-11}\)

8.5812\(\times 10^{-12}\)

3.0

2.99

− 6.6989\(\times 10^{-13}\)

− 6.1689\(\times 10^{-13}\)

5.2999\(\times 10^{-14}\)