Journal of Applied Mathematics / 2012 / Article / Tab 1

Research Article

Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

Table 1

Comparison of solutions to the macro-model with those to the micro-model for different values of πœ€ with data as in Example 3.2.

# cells πœ€ β€– 𝑒 𝑁 πœ€ β€– βˆ— , 𝐿 1 𝛼 1 β€– 𝑒 𝑁 πœ€ β€– βˆ— , 𝐿 2 𝛼 2

3 Γ— 3 1 / 3 1 . 1 8 3 2 Γ— 1 0 βˆ’ 2 β€” 3 . 2 0 7 1 Γ— 1 0 βˆ’ 2 β€”
5 Γ— 5 1 / 5 7 . 0 9 1 5 Γ— 1 0 βˆ’ 3 1 . 0 1 8 8 1 . 9 0 4 4 Γ— 1 0 βˆ’ 2 1 . 0 3 9 0
7 Γ— 7 1 / 7 5 . 0 5 2 2 Γ— 1 0 βˆ’ 3 1 . 0 0 7 7 1 . 3 5 2 8 Γ— 1 0 βˆ’ 2 1 . 0 1 6 4
9 Γ— 9 1 / 9 3 . 9 2 8 5 Γ— 1 0 βˆ’ 3 1 . 0 0 1 1 1 . 0 5 0 2 Γ— 1 0 βˆ’ 2 1 . 0 0 7 5
1 1 Γ— 1 1 1 / 1 1 3 . 2 1 6 2 Γ— 1 0 βˆ’ 3 0 . 9 9 6 9 8 . 5 8 9 0 Γ— 1 0 βˆ’ 3 1 . 0 0 2 1