Fix Docs Mistakes

[arnavs]

PR to fix mistakes in documentation.

• Looks like the README.md and individual docstrings are fine, so we just needed to patch the examples on index.md of the docs website.

[arnavs]

@chiyahn I still want to give this another look, but wanted to post so as to avoid a bottleneck. If you think we are good, then when I'm done, we can push and retag.

[codecov-io]

Codecov Report

Merging #121 into master will not change coverage. The diff coverage is n/a.

@@          Coverage Diff          @@
##           master   #121   +/-   ##
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  Coverage     100%   100%           
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  Files           4      4           
  Lines         108    108           
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  Hits          108    108

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[chiyahn]

Codes look good to me. One more thing: you need to update the resulting plot as well (as implementation has slightly changed.)

[arnavs]

Roger. You mean this bit? plot(x, v, lw = 4, label = "v")

I think this OK, since v is evaluated on the interior nodes x, right? But feel free to push to this branch with fixes and merge whenever you think we're good.

[chiyahn]

No, I mean the implementation for $L_2$ is different so that the resulting plot for v is going to be different in the new version as well.

[chiyahn]

I'll push the new plots

[arnavs]

Oh, I see. You're including a static image. OK, will do.

Edit: Thanks, will let you push.

[arnavs]

We should probably also change this text, but I'll defer to you on that:

One can alternatively use differential operators on interior nodes and stack them with matrices for boundary conditions to compute v:

Since we're still passing in x\bar.

[chiyahn]

Oh, actually nevermind for plots. I can confirm that they return the same plots since it's being computed from extension operators rather than operators on interior nodes with bc.

We should probably also change this text, but I'll defer to you on that:

One can alternatively use differential operators on interior nodes and stack them with matrices for boundary conditions to compute v:

Since we're still passing in x\bar.

I agree, I'll make a fix and merge the PR

[arnavs]

Thanks @chiyahn, will leave this in your hands then.