Generalized Diffusion Operator

Available identifiers

generalized version of the diffusion operator

Defining Formula: $\begin{aligned} \tilde{𝒟} f (𝐧, 𝐦) : \equiv & \frac{D_{A}}{h^{2}} \sum_{i = 1}^{K_{A} - 1} {(n_{i} + 1) f (𝒪_{i}^{+} 𝒪_{i + 1}^{-} 𝐧, 𝐦) - n_{i} f (𝐧, 𝐦)} \\ + \frac{D_{A}}{h^{2}} \sum_{i = 2}^{K_{A}} {(n_{i} + 1) f (𝒪_{i}^{+} 𝒪_{i - 1}^{-} 𝐧, 𝐦) - n_{i} f (𝐧, 𝐦)} \\ + \frac{D_{B}}{h^{2}} \sum_{i = 1}^{K_{B} - 1} {(m_{i} + 1) f (𝐧, 𝒪_{i}^{+} 𝒪_{i + 1}^{-} 𝐦) - m_{i} f (𝐧, 𝐦)} \\ + \frac{D_{B}}{h^{2}} \sum_{i = 2}^{K_{B}} {(m_{i} + 1) f (𝐧, 𝒪_{i}^{+} 𝒪_{i - 1}^{-} 𝐦) - m_{i} f (𝐧, 𝐦)} \end{aligned}$

Diffusion Operator