I wrote some codes but the plot is not continuous.
How to fix the problem?
What version are you running? Under version 13.2 your plot is continuous and looks fine.
You do notice that you have PlotStyle->{Dashing[Block],Black} Do you really want a dashed plot when you are asking why you are seeing gaps in your plot, but I don’t think that is your issue?
What happens if you include PlotPoints->100 or PlotPoints->250 to increase the number of sampling points? Pushing that up too much will slow it down, but may improve the quality.
i doesn’t solve the problem.
What is the meaning of Dashing[Block]? What is the 12 in Directive[Black, 12]? Did you mean to specify the Thickness? That’s not the way to do it. Your function l[r] behaves very differently with exact rational values of r and with floating-point values. Compare the time it takes for l[.5] and for l[1/2]. Why do you resort to ListLinePlot with rational values of r and not just do this:
Plot[l[r], {r, .01, .8}, PlotStyle -> Black, PlotRange -> {0, 0.5},
Frame -> True, RotateLabel -> False,
FrameStyle -> Directive[Black, Thickness[.004]],
FrameLabel -> {Style["r", 13, Bold, Black],
Style["N", 13, Bold, Black]},
PlotLabel -> Style["b", 13, Bold, Black]]
