$z^{*}$

Concentration $C^{*}$

when $\beta =0.5$

when $\beta =1$

when $\beta =1.6$

Equation (14)

Simulation

% of error deviation

Equation (14)

Simulation

% of error deviation

Equation (14)

Simulation

% of error deviation

0

1.0000

1.0000

0.00

1.0000

1.0000

0.00

1.0000

1.0000

0.00

0.2

0.8933

0.8929

0.04

0.9405

0.9411

0.06

0.9971

0.9971

0.00

0.4

0.7866

0.7859

0.08

0.8810

0.8822

0.13

0.9943

0.9942

0.01

0.6

0.6800

0.6788

0.17

0.8215

0.8233

0.21

0.9914

0.9914

0.00

0.8

0.5733

0.5717

0.27

0.7620

0.7644

0.31

0.9886

0.9885

0.01

1

0.472

0.4700

0.42

0.7055

0.7055

0.00

0.9857

0.9858

0.01

Average error % 0.163

Average error % 0.118

Average error % 0.005