Table 1 Boundary conditions and corresponding basis functions that obey these boundary conditions.
From: A new approach for simulating inhomogeneous chemical kinetics
Boundary conditions | Basis function | \(\omega _n\) |
|---|---|---|
\(\rho (0,t) = 0, \quad \frac{\partial \rho }{\partial x}(L,t) = 0\) | \(\sin (\omega _n x)\) | \(\frac{\pi }{L}\left( n + \frac{1}{2} \right)\) |
\(\frac{\partial \rho }{\partial x}(0,t) = 0, \quad \rho (L,t) = 0\) | \(\cos (\omega _n x)\) | \(\frac{\pi }{L}\left( n + \frac{1}{2} \right)\) |
\(\rho (0,t) = 0, \quad \rho (L,t) = 0\) | \(\sin (\omega _n x)\) | \(\frac{\pi }{L}n\) |
\(\frac{\partial \rho }{\partial x}(0,t) = 0, \quad \frac{\partial \rho }{\partial x}(L,t) = 0\) | \(\cos (\omega _n x)\) | \(\frac{\pi }{L}n\) |
