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I already tried solutions given in 2 similar questions: TikZ Picture in Table and Tikz Inside Table Cell but they do not seem to work for me.

Below I give MWE and what I tried. I have a tikz picture inside a long table cell. I want it to automatically fit into the width of the cell.

When using an actual image and includegraphics I would adjust the width manually to make it fit. But do not know how to do it for a tikz pic.

I am also using the "m" option for the cell, to make the image align OK with text in other cells. But if I remove the "m" option and put back the "p" option on that cell, it makes no difference for the tikz scaling.

MWE

documentclass[11pt]article 
usepackageamsmath,mathtools,amssymb 
ifdefinedHCode %Michal's driver for tex4ht use
 defpgfsysdriverpgfsys-dvisvgm4ht.def
fi 
usepackagetikz,graphicx,tikz-dependency
usetikzlibraryfit
usepackagelongtable
usepackagearray %for the m option on cells 
begindocument

beginlongtable[c]p0.5inhline
A&
Heat PDE in bar (1D)&
begintikzpicture[baseline=(current bounding box.center)]
coordinate[label =above:$0$, label =below:$u=0$] (A) at (0,0);
coordinate[label =above:$pi$, label =below:$u_x=0$] (B) at (4,0);

draw (A) -- node[above] $u_t = k u_xx $ node[below] $f(x)$ ++ (B);

node at (A)[circle,fill,inner sep=1pt];
node at (B)[circle,fill,inner sep=1pt]; 
%addvmargin1mm %has no effect if I uncomment it
endtikzpicture 

(Haberman 2.3.3 (a))&
B&0.415&C&2.376&Yes\hline
endlongtable 
enddocument

How to scale the tikz pic size to automatically fit into a table cell?

Compiled using lualatex foo2.tex using Using TL 2019 on linux.

lualatex foo2.tex
This is LuaTeX, Version 1.10.0 (TeX Live 2019)
 restricted system commands enabled.

I guess that this must be some sort of a duplicate answer but anyway adjustbox is made for such things. Note that if you do that, you should not use remember picture and try to access the coordinates from "outside". And adjustbox comes with its own mechanisms of vertical or horizontal alignment, but not using any seems to work fine. In any case, you should not expect baseline=(current bounding box.center) to work properly here either. In a way, the tikzpicture will behave as a graphics included with includegraphics, but if that's what you want then adjustbox seems to be the right tool.

documentclass[11pt]article 
usepackageamsmath,mathtools,amssymb 
ifdefinedHCode %Michal's driver for tex4ht use
 defpgfsysdriverpgfsys-dvisvgm4ht.def
fi 
usepackagetikz,tikz-dependency
usetikzlibraryfit
usepackagelongtable
usepackagearray %for the m option on cells 
usepackageadjustbox 
begindocument

beginlongtable[c]p0.5inhline
A&
Heat PDE in bar (1D)&
adjustboxmax width=1.2inbegintikzpicture

coordinate[label =above:$0$, label =below:$u=0$] (A) at (0,0);
coordinate[label =above:$pi$, label =below:$u_x=0$] (B) at (0.95in,0);

draw (A) -- node[above] $u_t = k u_xx $ node[below] $f(x)$ ++ (B);

node at (A)[circle,fill,inner sep=1pt];
node at (B)[circle,fill,inner sep=1pt]; 
%addvmargin1mm %has no effect if I uncomment it
endtikzpicture 

(Haberman 2.3.3 (a))&
B&0.415&C&2.376&Yes\hline
endlongtable 
enddocument

Addendum: as mentioned above you can rewrite the tikzpicture in such a way that it has the desired width. However, this is not a general solution. I am adding this merely to say that there is no need to introduce ad hoc distances like 0.6linewidth, but you do have to look at the picture and find out which are the left-most and right-most nodes (u=0 and u_x=0 in this case). One can then start with those "extremal nodes", use appropriate anchors (along with outer sep=0pt) to place them such that the picture has the right width, and then add the rest relative to them.

documentclass[11pt]article 
usepackageamsmath,mathtools,amssymb 
ifdefinedHCode %Michal's driver for tex4ht use
 defpgfsysdriverpgfsys-dvisvgm4ht.def
fi 
usepackagetikz,tikz-dependency
usetikzlibraryfit
usepackagelongtable
usepackagearray %for the m option on cells 
usepackageadjustbox 
begindocument

beginlongtable[c]p0.5inhline
A&
Heat PDE in bar (1D)&
begintikzpicture[baseline=(current bounding box.center),nodes=outer xsep=0pt]
node[anchor=west] (A0) at (0,0) $u=0$;
node[anchor=east] (B0) at (linewidth,0) $u_x=0$;
node[label=above:$0$] (A) at ([yshift=0.2ex]A0.north) [circle,fill,inner sep=1pt];
node[label =above:$pi$] (B) at (B0|-A) [circle,fill,inner sep=1pt]; 
draw (A) -- node[above] $u_t = k u_xx $ node[below] $f(x)$ ++ (B);
endtikzpicture 

(Haberman 2.3.3 (a))&
B&0.415&C&2.376&Yes\hline
endlongtable 
enddocument

make image width(determined with line length + width of nodes) dependent from cell width:

documentclass[11pt]article
usepackagegeometry
usepackagemathtools,amssymb
ifdefinedHCode %Michal's driver for tex4ht use
 defpgfsysdriverpgfsys-dvisvgm4ht.def
fi
usepackagetikz,graphicx,tikz-dependency
usetikzlibraryfit,
 positioning,
 quotes
usepackagearray, longtable
%---------------- show page layout. don't use in a real document!
usepackageshowframe
renewcommandShowFrameLinethickness0.15pt
renewcommand*ShowFrameColorcolorred

begindocument
begingroup
beginlongtablehline
A & Heat PDE in bar (1D)
 & begintikzpicture[baseline=(current bounding box.base),
 every node/.append style = font=footnotesize,
 dot/.style = circle, fill, inner sep=2pt
 ]
 node (A) [dot,label=$0$, label=below:$u=0$] ;
 node (B) [dot,label=$pi$, label=below:$u_x=0$,
 right=0.6linewidth of A] ; % <---
 draw (A) to ["$u_t=k u_xx$","$f(x)$" '](B);
 endtikzpicture

(Haberman 2.3.3 (a))
 & B & 0.415 & C & 2.376 & Yes \
 hline
endlongtable
endgroup
enddocument