Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Results for different $\underset{}{ε}$ and ε_k+1(u⁽⁰⁾ = 0)

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

$N = 256; u = u 1; σ (u) = σ 1; ṽ_{1} = ṽ_{2} = 1; τ = 1 0^{- 3}; r e s 0 = 205.61$
$\underset{}{ε}$	k *	j _T	*err*	*res*
10^-3	15	210	4.21(-6)	1.20(-3)
10^-4	18	260	5.26(-7)	1.51(-4)
10^-5	21	310	6.59(-8)	1.90(-5)
10^-6	25	377	4.09(-9)	1.18(-6)
$N = 256; u = u 1; σ (u) = σ 1; ṽ_{1} = ṽ_{2} = 1; τ = 1 0^{- 3}; r e s 0 = 205.61$
ε _k+1	k*	j _T	err	res
0.7ε_k	35	268	3.85(-7)	1.10(-4)
0.5ε_k	18	260	5.26(-7)	1.51(-4)
0.1 ε_k	6	250	7.08(-7)	2.01(-4)
0.05ε_k	5	260	4.36(-7)	1.23(-4)
0.01ε_k	3	189	7.67(-6)	2.31(-3)
$N = 256; u = u 4; σ (u) = σ 1; ṽ_{1} = ṽ_{2} = 1; τ = 1 0^{- 3}; r e s 0 = 9617.82$
ε _k+1	k*	j _T	err	res
0.7ε_k	46	1625	3.10(-7)	1.02(-4)
0.5ε_k	24	1607	3.46(-7)	1.13(-4)
0.1 ε	7	1327	3.06(-6)	9.34(-4)
0.05ε_k	6	1408	1.02(-6)	3.09(-4)
0.01 ε_k	4	1384	4.12(-5)	2.46(-2)
$N = 256; u = u 4; σ (u) = σ 2; ṽ_{1} = ṽ_{2} = 1; τ = 1 0^{- 3}; r e s 0 = 31481.01$
ε _k+1	k*	j _T	err	res
0.7ε_k	49	4146	2.78(-7)	1.14(-4)*
0.5ε_k	25	3960	4.70(-7)	1.85(-4)*
0.1 ε_k	8	4930	1.75(-5)	1.42(-2)*
0.05ε_k	6	4827	3.16(-4)	0.27*
0.01 ε_k	4	3800	4.70(-3)	4.63*

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