Table 1 Comparison of localized solution with approximate solution for \(\mu _0=1\),and \(\bar{\tau } (=\tau \omega _0)=0.1\).

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

− 3.1

− 2.2648\(\times 10^{-13}\)

− 5.0807\(\times 10^{-13}\)

2.816\(\times 10^{-13}\)

− 2.5

− 2.6

− 3.132\(\times 10^{-11}\)

− 8.2781\(\times 10^{-11}\)

5.146\(\times 10^{-11}\)

− 2.0

− 2.1

− 4.3314\(\times 10^{-09}\)

− 1.1595\(\times 10^{-08}\)

7.2638\(\times 10^{-09}\)

− 1.5

− 1.6

− 5.9901\(\times 10^{-07}\)

− 1.6053\(\times 10^{-06}\)

1.0063\(\times 10^{-06}\)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

\(\cdots \)

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1.5

1.4

− 4.3028\(\times 10^{-06}\)

− 1.6056\(\times 10^{-06}\)

2.6972\(\times 10^{-06}\)

2.0

1.9

− 3.1114\(\times 10^{-08}\)

− 1.1623\(\times 10^{-08}\)

1.9491\(\times 10^{-08}\)

2.5

2.4

− 2.2498\(\times 10^{-10}\)

− 8.5107\(\times 10^{-11}\)

1.3988\(\times 10^{-11}\)

3.0

2.9

− 1.6268\(\times 10^{-12}\)

− 7.0592\(\times 10^{-13}\)

9.2093\(\times 10^{-13}\)