Theory and Modern Applications

# Table 5 Table of absolute errors in the maximum norm and spatial rates of convergence for various values of the parameters τ and h. We used $$f (u) = u (1 - u)$$, and the exact solution (58) of model (46). We employed also $$\varOmega = (- 200, 200)$$ and various values of T

τ = 5 × 10−4

τ = 2.5 × 10−4

τ = 1.25 × 10−4

h

$$\epsilon _{t, h}$$

$$\rho _{h}$$

$$\epsilon _{t, h}$$

$$\rho _{h}$$

$$\epsilon _{t, h}$$

$$\rho _{h}$$

T = 1

2/20

2.72891640 × 10−3

7.38903899 × 10−4

1.92801667 × 10−4

2/21

6.08617515 × 10−4

2.16472044

1.53496126 × 10−4

2.26718449

4.23532511 × 10−5

2.18657290

2/22

1.23264181 × 10−4

2.30378222

3.31398131 × 10−5

2.21156488

9.55526103 × 10−6

2.14810553

2/23

2.40756903 × 10−5

2.35610456

6.97944970 × 10−6

2.24738027

2.24943767 × 10−6

2.08673089

2/24

5.35953443 × 10−6

2.16739758

1.57552357 × 10−6

2.14728195

5.00208668 × 10−7

2.16896243

T = 10

2/20

2.80627843 × 10−3

7.48551627 × 10−4

2.18637328 × 10−4

2/21

5.82837716 × 10−4

2.26749201

1.66642570 × 10−4

2.16734482

5.11309655 × 10−5

2.09627056

2/22

1.29375821 × 10−4

2.17152622

3.94539680 × 10−5

2.07851469

1.13824890 × 10−5

2.16738120

2/23

2.71945685 × 10−5

2.25017758

9.26898876 × 10−6

2.08968655

2.60012534 × 10−6

2.13016299

2/24

6.35975778 × 10−6

2.09627481

2.13604753 × 10−6

2.11746820

6.21903759 × 10−7

2.06381793

T = 50

2/20

2.87820224 × 10−3

7.53867720 × 10−4

2.24422947 × 10−4

2/21

6.50328970 × 10−4

2.14592637

1.66761373 × 10−4

2.17652624

5.03484551 × 10−5

2.15620078

2/22

1.53265284 × 10−4

2.08513874

3.84354956 × 10−5

2.11727398

1.18548423 × 10−5

2.08647103

2/23

3.65707445 × 10−5

2.06726905

9.18431827 × 10−6

2.06519473

2.82647735 × 10−6

2.06839944

2/24

8.84445865 × 10−6

2.04784425

2.22227666 × 10−6

2.04713420

6.81731460 × 10−7

2.05172967 