Skip to main content

Theory and Modern Applications

Table 3 Solution and residual error for Example 3 when \(\alpha =0.9\) and \(\beta =0.3\) at several values of x and t using 60 terms of the series (\(\hbar =-0.55\))

From: Homotopy-Sumudu transforms for solving system of fractional partial differential equations

x

 

t

 

0

0.2

0.4

0.6

0.8

1

0

u

1.0000

1.1712

1.3467

1.5670

1.8569

2.2501

Eu

0

1.110 10−16

1.810 10−14

3.628 10−12

1.069 10−9

1.0219 10−7

0.25

u

1.2840

1.5260

1.7759

2.0839

2.4809

3.0088

Eu

1.110 10−16

3.331 10−16

2.365 10−14

4.828 10−12

1.363 10−9

1.263 10−7

0.5

u

1.6487

1.9817

2.3270

2.7476

3.2822

3.9831

Eu

0

5.551 10−17

2.903 10−14

6.234 10−12

1.748 10−9

1.504 10−7

0.75

u

2.1170

2.5668

3.0346

3.5998

4.3110

5.2340

Eu

0

6.106 10−16

3.325 10−14

8.418 10−12

2.253 10−9

1.888 10−7

1

u

2.7183

3.3180

3.9432

4.6940

5.6321

6.8402

Eu

0

2.220 10−16

4.0468 10−14

1.0858 10−11

2.895 10−9

2.451 10−7

0

v

1.0000

0.44309

0.37067

0.34020

0.33444

0.35088

Ev

0

1.110 10−16

2.665 10−15

2.505 10−12

2.906 10−10

3.565 10−9

0.25

v

0.77880

0.31806

0.26122

0.24137

0.24388

0.26700

Ev

1.110 10−16

1.110 10−16

2.665 10−15

2.240 10−12

2.628 10−10

5.915 10−9

0.5

v

0.60653

0.22068

0.17598

0.16441

0.17335

0.20168

Ev

0

2.220 10−16

2.776 10−15

2.120 10−12

2.205 10−10

6.812 10−9

0.75

v

0.47237

0.14484

0.10959

0.10446

0.11842

0.15080

Ev

0

3.331 10−16

3.553 10−15

1.892 10−12

1.778 10−10

9.974 10−9

1

v

0.36788

0.085772

0.057893

0.057780

0.075645

0.11118

Ev

0

2.220 10−16

4.996 10−15

1.860 10−12

1.895 10−10

9.886 10−9