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Theory and Modern Applications

Table 1 Numerical results of the FRPS solutions at different values of t of Example 4.1

From: Construction of fractional power series solutions to fractional stiff system using residual functions algorithm

t

Exact u(t)

Approximation u(t)

Absolute Error

Relative Error

0.000

1.

1.

0.

0.

0.025

1.830049650419

1.8300496504186

6.661338147751 × 10−16

3.639976732996 × 10−16

0.050

1.820521847980

1.8205218479801

4.218847493576 × 10−15

2.317383610780 × 10−15

0.075

1.7389664179059

1.7389664179059

1.998401444325 × 10−15

1.149189210181 × 10−15

0.100

1.6548121396395

1.6548121396396

6.017408793468 × 10−14

3.636309312294 × 10−14

0.125

1.574165520630

1.5741655206310

1.418198891656 × 10−12

9.009210740996 × 10−13

0.150

1.4973979619154

1.4973979619805

6.508638072944 × 10−11

4.346632116834 × 10−11

0.175

1.4243694914073

1.4243694910746

3.326674491433 × 10−10

2.335541803936 × 10−10

0.200

1.3549022160256

1.3549022084615

7.564062487475 × 10−9

5.582736818944 × 10−9

0.225

1.2888228592360

1.2888227498472

1.093887884718 × 10−7

8.487495988131 × 10−8

0.250

1.2259662270401

1.2259657966770

4.303631988556 × 10−7

3.510400118400 × 10−7

t

Exact v(t)

Approximation v(t)

Absolute Error

Relative Error

0.000

1.

1.

0.

0.

0.025

0.0724091985828

0.0724091985828

2.3592239273 × 10−16

3.2581826253 × 10−15

0.050

−0.010847011908

−0.010847011908

3.2734231992 × 10−15

3.0178110130 × 10−13

0.075

−0.0175504650558

−0.0175504650558

1.3850032232 × 10−14

7.8915471403 × 10−13

0.100

−0.0173506334835

−0.0173506334839

3.6409417148 × 10−13

2.0984488654 × 10−11

0.125

−0.0165639544868

−0.0165639544956

8.8100464424 × 10−12

5.3188062364 × 10−10

0.150

−0.0157615205520

−0.0157615206823

1.3034362131 × 10−10

8.2697364688 × 10−9

0.175

−0.0149933119699

−0.0149933122356

2.6574836429 × 10−10

1.7724460401 × 10−8

0.200

−0.0142621239543

−0.0142621227122

1.2421122308 × 10−9

8.7091672654 × 10−8

0.225

−0.0135665559925

−0.0135665780247

2.2032217302 × 10−8

1.6240096100 × 10−6

0.250

−0.0129049076149

−0.0129052984430

3.9082809609 × 10−7

3.0285230070 × 10−5