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Table 2 Comparison solution by MDTM, FDM, and shooting method with GM, LSM, and CM [32] for V (η) when \(\varphi\) = 0.01, δ = 1, P = 0, Ha = 3, Rd = 2, Ec = 1, Pr = 6.2, and \(\alpha\) = 0

From: Radiative MHD flow of Rivlin–Ericksen nanofluid of grade three through porous medium with uniform heat source

η

Present v (η)

v (η) [32]

MDTM

FDM

Shooting method

G.M

L.S.M

C.M

 − 1

0

0

0

0

0

0

 − 0.9

0.008927973453246

0.008787225412899

0.008957094

0.007785

0.008539

0.006847

 − 0.8

0.014223686772939

0.013959477936244

0.014244837

0.013111

0.014381

0.011531

 − 0.7

0.016769654790264

0.016440045972315

0.016784495

0.016252

0.017827

0.014294

 − 0.6

0.017266325478027

0.016922743531933

0.017251388

0.017481

0.019175

0.015375

 − 0.5

0.016255425114184

0.015931229672889

0.016188057

0.017072

0.018726

0.015014

 − 0.4

0.014150728407177

0.013863775889415

0.014023246

0.015296

0.016779

0.013453

 − 0.3

0.011268952330109

0.011027308517539

0.011090881

0.012428

0.013633

0.010931

 − 0.2

0.007857588237348

0.007663635866098

0.007649044

0.008741

0.009589

0.007687

 − 0.1

0.004116729433862

0.003970101131019

0.003898955

0.004507

0.004945

0.003964

0

0.000217343161713

0.000116424993575

3.9459E06

4.23 × 10−7

1.54 × 10−6

1.81 × 10−9

0.1

 − 0.003683298028354

 − 0.003740824702763

 − 0.003891557

 − 0.00451

 − 0.00494

 − 0.00396

0.2

 − 0.007427456163251

 − 0.007444902635067

 − 0.007643058

 − 0.00874

 − 0.00959

 − 0.00769

0.3

 − 0.010842771287347

 − 0.010825560149113

 − 0.011087014

 − 0.01243

 − 0.01363

 − 0.01093

0.4

 − 0.013726806197571

 − 0.013684591023138

 − 0.014021855

 − 0.0153

 − 0.01678

 − 0.01345

0.5

 − 0.015828922831118

 − 0.015779021734224

 − 0.016189006

 − 0.01707

 − 0.01872

 − 0.01501

0.6

 − 0.016828099926917

 − 0.016800520671318

 − 0.017253911

 − 0.01748

 − 0.01917

 − 0.01537

0.7

 − 0.016305660627378

 − 0.016349281399216

 − 0.016787055

 − 0.01625

 − 0.01783

 − 0.01429

0.8

 − 0.0137132512402211

 − 0.013900167871314

 − 0.014244981

 − 0.01311

 − 0.01438

 − 0.01153

0.9

 − 0.0083405628843889

 − 0.008758254914885

 − 0.008951319

 − 0.00778

 − 0.00854

 − 0.00685

1

0.0007030694820217

0

0

0

0

0