Journal of Applied Mathematics / 2012 / Article / Tab 3

Research Article

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

Table 3

Comparison of the macro-model to the micro-model for different values of πœ€ Example 3.4.

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