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Theory and Modern Applications

Table 2 Results with N = 256, 1 = 2 =1, u(0) = e

From: Lagged diffusivity method for the solution of nonlinear diffusion convection problems with finite differences

u(x, y, t)

k*

j T

Err

res

res0

τ = 10-3

     

σ(u) = σ 1

     

   u 1

20

302

3.69(-7)

1.03(-4)

546.04

   u 2

26

6066

4.76(-7)

1.47(-4)

50940.66

   u 3

20

633

4.63(-7)

1.31(-4)

692.97

   u 4

24

1631

3.37(-7)

1.10(-4)

9323.23

σ(u) = σ 2

     

   u 1

19

249

4.51(-7)

1.32(-4)

362.86

   u 2

29

38837

2.36(-7)

1.06(-4)*

298830.38

   u 3

20

932

5.45(-7)

1.67(-4)

881.87

   u 4

26

4122

2.63(-7)

1.03(-4)*

35275.82

τ = 10-4

     

σ(u) = σ 1

     

   u 1

18

37

5.17(-7)

1.34(-4)

211.75

   u 2

23

737

5.23(-7)

1.40(-4)

6026.72

   u 3

18

76

3.73(-7)

9.89(-5)

132.60

   u 4

21

240

3.46(-7)

1.00(-4)

1074.69

σ(u) = σ 2

     

   u 1

18

33

4.50(-7)

1.19(-4)

205.39

   u 2

25

7615

5.02(-7)

1.68(-4)*

30266.34

   u 3

18

121

3.82(-7)

1.05(-4)

144.41

   u 4

22

910

4.89(-7)

1.69(-4)

3611.96

σ(u) = σ 3

     

   u 2

22

48

3.98(-7)

1.24(-4)

2825.73

   u 3

17

102

4.76(-7)

1.66(-4)

113.34

   u 4

19

604

3.99(-7)

1.58(-4)

416.74