Table 4 Comparison of exact and approximate solution of Example  4 using the boundary condition as defined in \(\pmb{\mathbf{S_{2}}}\)

t = 0.0

1.0000000000

0.9993612934

1.0001381646

1.0000260271

1.000000020

t = 0.1

1.0168063300

1.1131408265

1.0322239559

1.0171510593

1.016806465

t = 0.2

1.0338951135

1.2060058045

1.0595571295

1.0344373486

1.033895324

t = 0.3

1.0512710963

1.2803801650

1.0835040499

1.0519291558

1.051271352

t = 0.4

1.0689391057

1.3388134647

1.1052061945

1.0696628704

1.068939387

t = 0.5

1.0869040495

1.3839808784

1.1255801546

1.0876670104

1.086904346

t = 0.6

1.1051709180

1.4186831997

1.1453176345

1.1059622221

1.105171226

t = 0.7

1.1237447856

1.4458468410

1.1648854519

1.1245612803

1.123745105

t = 0.8

1.1426308117

1.4685238330

1.1845255377

1.1434690886

1.142631142

t = 0.9

1.1618342427

1.4898918253

1.2042549363

1.1626826787

1.161834578

t = 1.0

1.1813604128

1.5132540859

1.2238658054

1.1821912111

1.181360731