# Stability plot of upward difference implicit time

I am analyzing the stability of 1D convection (advection) equation as shown in the picture. When I derive the equations as shown I want to get rid of the complex number. Im asking if those stability plots make sense or not

I want to get rid of a complex number

• Can you please type your equations using MathJax? – nicoguaro Apr 8 at 16:28
• ok, sure, but Im asking about the graphs, is it correct that as the wave numbers increase the amplification factor goes far from One? – Abdelrahman Mabrouk Apr 8 at 16:50
• I don't think so, you need to compute the magnitude of $\gamma$ and then consider the maximum/minimum value of your trigonometric functions. – nicoguaro Apr 8 at 17:52