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Theory and Modern Applications

Table 5 Results with N=256, 1 = 2 =1, u ( 0 ) = u n ,w= w n

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

u(x, y, t)

σ ̄ * / 1

k*

j T

E step

res

res0

w*-wn

τ = 10-3

       

σ(u) = σ 1

       

   u 1

0.51

9

143

4.84(-7)

1.37(-4)

0.36

1.16(-12)

   u 2

8.52

17

3850

7.25(-5)

1.01(-4)

68.40

3.58(-2)

   u 3

1.01

11

341

6.78(-7)

1.89(-4)

1.97

3.51(-12)

   u 4

4.01

15

967

2.65(-7)

1.15(-4)

19.05

8.34(-5)

σ(u) = σ 2

       

   u 1

0.51

9

120

3.97(-7)

1.18(-4)

0.31

9.75(-13)

   u 2

145.03

20

17950

1.94(-4)

1.32(-4)

734.79

7.13(-1)

   u 3

2.01

12

538

5.24(-7)

1.58(-4)

3.27

6.79(-12)

   u 4

32.01

17

2452

2.46(-6)

1.88(-4)

125.38

1.50(-3)

τ = 10-4

       

σ(u) = σ 1

       

   u 1

0.51

4

12

4.06(-7)

1.07(-4)

9.63(-3)

1.17(-13)

   u 2

8.52

10

341

1.24(-5)

1.39(-4)

0.73

3.56(-3)

   u 3

1.01

6

30

4.05(-7)

1.06(-4)

3.56(-2)

3.52(-13)

   u 4

4.01

8

95

5.35(-7)

1.58(-4)

0.20

8.34(-6)

σ(u) = σ 2

       

   u 1

0.51

4

10

4.29(-7)

1.15(-4)

9.37(-3)

9.86(-14)

   u 2

145.03

13

3585

1.01(-4)

1.67(-4)

7.36

7.13(-2)

   u 3

2.01

6

46

5.12(-7)

1.39(-4)

4.49(-2)

6.81(-13)

   u 4

32.01

11

413

2.84(-7)

1.23(-4)

1.26

1.50(-4)

σ(u) = σ 3

       

   u 2

1.50

8

15

5.68(-7)

1.43(-4)

0.21

7.58(-5)

   u 3

100.00

6

19

1.08(-6)

1.00(-4)

3.38(-2)

1.86(-2)

   u 4

100.00

6

24

5.22(-7)

1.66(-4)

5.49(-2)

8.45(-5)