I`m Analyzing the 1D convection equation (PDE) for stability, consistency, and accuracy.

I know Both upwind schemes (explicit and implicit) show better stability with a higher number of waves for courant number less than one. The upwind scheme, in general, overcomes the problem of stability in the centered difference scheme. However, the upwind schemes scarify some accuracy to gain stability.

Now I`m confused about the stability and accuracy of both the Centered difference – trapezoidal and Lax Wendroff Schemes.

I have attached photos of the analysis I conducted but not sure how to comment. I`m also confused about the order of schemes of:

a) Backward difference – explicit time b) Backward difference – implicit time c) Centered difference – trapezoidal time d) Lax Wendroff

In the attached graphs Beta is courant number, N-lambda is no. of intervals per wave length, r is the amplification factor. 1 3 4 enter image description here

  • $\begingroup$ I am trying to figure out how to best answer you question but I am not sure you are defining a bunch of your plots. If you can provide code or equations that would be helpful. $\endgroup$ – Kyle Mandli Apr 18 at 23:33

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