Table 1 Adomian decomposition approachs outcome.

From: Novel insights into high-order dispersion and soliton dynamics in optical fibers via the perturbed Schrödinger–Hirota equation

Value of \(\xi\)

Exact sol.

Approx. sol.

Absolute error

Value of \(\xi\)

Exact sol.

Approx. sol.

Absolute error

\(-0.030\)

0.775258744695

0.771788871147

3.4698735480E-03

0.001

1.00852138341

1.00851636004

5.0233700000E-06

\(-0.029\)

0.781865021704

0.778569547058

3.2954746460E-03

0.002

1.0171153808

1.01709519531

2.0185490000E-05

\(-0.028\)

0.788527593331

0.785408113907

3.1194794240E-03

0.003

1.02578261094

1.02573698955

4.5621390000E-05

\(-0.027\)

0.795246939287

0.792304127249

2.9428120380E-03

0.004

1.03452369787

1.03444223526

8.1462610000E-05

\(-0.026\)

0.802023543365

0.799257212696

2.7663306690E-03

0.005

1.04333927095

1.04321143287

1.2783808000E-04

\(-0.025\)

0.808857893485

0.806267061358

2.5908321270E-03

0.006

1.05222996491

1.05204509038

1.8487453000E-04

\(-0.024\)

0.815750481723

0.813333425592

2.4170561310E-03

0.007

1.06119641988

1.06094372255

2.5269733000E-04

\(-0.023\)

0.822701804348

0.82045611498

2.2456893680E-03

0.008

1.07023928145

1.06990785055

3.3143090000E-04

\(-0.022\)

0.829712361858

0.82763499262

2.0773692380E-03

0.009

1.07935920071

1.07893800143

4.2119928000E-04

\(-0.021\)

0.836782659016

0.834869971626

1.9126873900E-03

0.010

1.0885568343

1.08803470752

5.2212678000E-04

\(-0.020\)

0.843913204889

0.842161011894

1.7521929950E-03

0.011

1.09783284445

1.09719850619

6.3433826000E-04

\(-0.019\)

0.851104512875

0.849508117011

1.5963958640E-03

0.012

1.10718789905

1.10642993924

7.5795981000E-04

\(-0.018\)

0.858357100755

0.856911331456

1.4457692990E-03

0.013

1.11662267164

1.11572955269

8.9311895000E-04

\(-0.017\)

0.865671490716

0.864370737897

1.3007528190E-03

0.014

1.12613784156

1.12509789635

1.0399452100E-03

\(-0.016\)

0.873048209399

0.871886454723

1.1617546760E-03

0.015

1.13573409388

1.13453552342

1.1985704600E-03

\(-0.015\)

0.880487787931

0.879458633682

1.0291542490E-03

0.016

1.14541211955

1.14404299025

1.3691293000E-03

\(-0.014\)

0.887990761963

0.887087457708

9.0330425500E-04

0.017

1.15517261539

1.15362085603

1.5517593600E-03

\(-0.013\)

0.895557671713

0.894773138863

7.8453285000E-04

0.018

1.16501628416

1.16326968255

1.7466016100E-03

\(-0.012\)

0.903189062003

0.902515916446

6.7314555700E-04

0.019

1.1749438346

1.1729900338

1.9538008000E-03

\(-0.011\)

0.910885482296

0.91031605518

5.6942711600E-04

0.020

1.1849559815

1.18278247589

2.1735056100E-03

\(-0.010\)

0.918647486737

0.91817384349

4.7364324700E-04

0.021

1.19505344575

1.19264757678

2.4058689700E-03

\(-0.009\)

0.926475634194

0.926089591991

3.8604220300E-04

0.022

1.20523695436

1.20258590596

2.6510484000E-03

\(-0.008\)

0.934370488296

0.934063631967

3.0685632900E-04

0.023

1.21550724055

1.21259803445

2.9092061000E-03

\(-0.007\)

0.942332617478

0.942096313995

2.3630348300E-04

0.024

1.22586504379

1.22268453438

3.1805094100E-03

\(-0.006\)

0.950362595015

0.950188006637

1.7458837800E-04

0.025

1.23631110984

1.23284597906

3.4651307800E-03

\(-0.005\)

0.958460999069

0.958339095237

1.2190383200E-04

0.026

1.24684619083

1.24308294257

3.7632482600E-03

\(-0.004\)

0.96662841273

0.966549980753

7.8431977000E-05

0.027

1.25747104528

1.25339599991

4.0750453700E-03

\(-0.003\)

0.974865424053

0.974821078703

4.4345350000E-05

0.028

1.26818643819

1.26378572658

4.4007116100E-03

\(-0.002\)

0.983172626109

0.983152818168

1.9807941000E-05

0.029

1.27899314107

1.27425269853

4.7404425400E-03

\(-0.001\)

0.991550617018

0.991545640801

4.9762169999E-06

0.030

1.28989193201

1.2847974922

5.0944398100E-03