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Table 2 Comparison between ( 20), exact solution (Erdogan and Ozis2011; Lin et al.2008), and other reported approximate solutions

From: Direct application of Padé approximant for solving nonlinear differential equations

x

Exact

This work

HPM

ADM

HPM

HPM

HAM

LDTM

 

(Erdogan and Ozis2011; Lin et al.2008)

(20)

(Vazquez-Leal et al.2012c)

(Deeba et al.2000)

(Feng et al.2007)

(Mirmoradia et al.2009)

(Hassana and El-Tawil2011)

(Khuri2003)

0.1

0.0959443493

0.0959443493

0.0959443155

0.0959383534

0.0959395656

0.095948026

0.0959446190

0.0959443520

0.2

0.1921287477

0.1921287477

0.1921286848

0.1921180592

0.1921193244

0.192135797

0.1921292845

0.1921287539

0.3

0.2887944009

0.2887944009

0.2887943176

0.2887803297

0.2887806940

0.288804238

0.2887952148

0.2887944107

0.4

0.3861848464

0.3861848464

0.3861847539

0.3861687095

0.3861675428

0.386196642

0.3861859313

0.3861848612

0.5

0.4845471647

0.4845471647

0.4845470753

0.4845302901

0.4845274183

0.4845599

0.4845485110

0.4845471832

0.6

0.5841332484

0.5841332484

0.5841331729

0.5841169798

0.5841127822

0.584145785

0.5841348222

0.5841332650

0.7

0.6852011483

0.6852011483

0.6852010943

0.6851868451

0.6851822495

0.685212297

0.6852028604

0.6852011675

0.8

0.7880165227

0.7880165227

0.7880164925

0.7880055691

0.7880018367

0.788025104

0.7880181729

0.7880165463

0.9

0.8928542161

0.8928542161

0.8928542059

0.8928480234

0.8928462193

0.892859085

0.8928553997

0.8928542363

 

Order

[12/12]

2

6

2

2

6

3

 

A.A.R.E.

0

1.83327e(-07)

3.47802e(-05)

3.57932e(-05)

2.44418e(-05)

2.51374e(-06)

3.10957e(-08)

  1. Calculated for n = 0.5.