@Rouben Rostamian  I missed your comment as I was writing my method. Perhaps my answer then is GIGO. It would be nice to have an analytical solution. I think in general an incompatiblilty in the initial condition can just indicate a step change (intended) in conditions at t=0, such as putting a uniform temperature object in contact with a freezer at t=0, forcing the boundary temperature immediately to a lower value. But I didn't think about the lack of a t derivative in this context.

@ijuptilk The theta(z,0) = thetab*sin(pi/2)*z IC is not compatible with the theta(d,t)=0 BC. Is this intended? And sin(pi/2)=1 so is this right?

@C_R Don't know much about Maplesim, but for electronics schematics (circuit diagrams), they moved away from arcs for non-crossing. They then went to a dot on the intersection if there was a connection, but the newer way is that connections are always at a T.

@nm Since v and theta are coupled, the time dependence of theta induces a time dependence of v. pdsolve (without any boundary/initial conditions) gives a general analytical solution where both theta and v are functions of z and t. Whether or not this solution can be made to fit the ic/bcs is not clear to me.

@mehdibgh Perhaps as a way to get initial guesses for fsolve, if the nonlinear problem is close to this...

@Christian Wolinski kk := Matrix(1, 8, {(1, 1) = .500000000000000+0.*I, (1, 2) = 0.1825477032e-15-.5879378012*I, (1, 3) = -.500000000000000+.555570233019603*I, (1, 4) = -0.2691433088e-15-.5879378012*I, (1, 5) = .500000000000000+0.*I, (1, 6) = -0.2691433088e-15+.587937801209679*I, (1, 7) = -.500000000000000-.5555702330*I, (1, 8) = 0.1825477032e-15+.587937801209679*I})

PDEtools:-casesplit seems to be for this purpose, but I've not used it.

@zenterix I was surprised to see the symbols in the plot of floor(x) - they seem to be an "added extra" just for floor(x). They can be enhanced by symbolsize = 20, symbol = solidcircle, but Maple doesn't seem to have them for more complicated functions. You could add symbols yourself by combining the line plot you have with plots with style=point, symbol=solidcircle and style=point, symbol=circle. The three plots could be combined using plots:-display. However, you would have to calculate the endpoints separately, and not using the floor function.

Edit: See plot,discont for more info on getting better discont detection and other options.

@vs140580 See ?ExcelTools,Export. Just write a row of the matrix (or a row vector), specifying the start cell for it.

@vs140580 Your matrix says it has dimensions 83,16, but when I copy it into Maple, I get an error saying it is actually 83x256. So I remove the "83,16" and then try to export the 83x256 Matrix to Excel. Now I get an error message saying the number of columns has to be 255 or less. I'm not sure if this is an Excel limitation, or limitation of my version of Maple (2015). Perhaps this will run for you. You could export the transposed Matrix, or export to another format, e.g., csv.

Excel2.mw

@vs140580 So for methanol you want to convert "CO" to a graph with two vertices and an edge between them?

pysmiles does this in python, though output is in networkx format. But I assume that the code could be fairly easily converted to Maple. 

IUPAC to SMILES (Simplified molecular-input line-entry system) is going to be difficult. For simple molecules, just search Wikipedia for the molecule (try methanol) and it likely has the SMILES string there on the right side of the page. SMILES is based on spanning trees with information on where the cycles are broken, so generating a graph from it should be straightforward. Likewise generating the missing hydrogens is straightforward. There is specialized software for this (the Wikipedia page may be a starting place for that; I don't have any experience with this). If you just want to draw the molecule, ChemDraw can take a SMILES string as input.

If you want a Maple Graph from SMILES, you will need to think more about it - how do you want to distinguish the vertices for different atoms, or is the bare connectivity all you want? What exactly do you mean by chemical graph?

@tomleslie My assumption is that there is a track along the curve. The ball is dropped (or more accurately thrown down, since initial velocity is non-zero) and rolls down the track; as the track curves it forces the x-direction to change. 

@JAMET Well, it's difficult to be sure because you didn't upload your worksheet, but the * after plots:-pointplot suggests you are using 2D input and have a space there that should not be there.

@Joe Riel Thanks; I'd never noticed that. I see now the help page has comptype with the key option more prominently explained than in my version.