@emma hassan Using the first table from your original post, I made it into a Matrix M as I described; and here is how to plot it:

plots:-surfdata(M, 0.05..0.85, 0.05..0.85, labels= [t,x,U], axes= boxed, title= "Crank-Nicolson");

@emma hassan Can you make the data into matrices? Or is it already in matrices in your worksheet? I don't need to have it; I just want to know if you have it. I used cut-and-paste from this blog, a bit of editting in Microsoft Notepad, and Maple's ImportData(). Once you have the matrices, I can tell you how to plot them. The matrices should not include the top rows of x-values nor the leftmost columns of t-values. 

@emma hassan Can you make the data into matrices? Or is it already in matrices in your worksheet? I don't need to have it; I just want to know if you have it. I used cut-and-paste from this blog, a bit of editting in Microsoft Notepad, and Maple's ImportData(). Once you have the matrices, I can tell you how to plot them. The matrices should not include the top rows of x-values nor the leftmost columns of t-values. 

@emma hassan In what form do your tables exist in the computer? As matrices, perhaps? Could you upload a worksheet that contains this data?

@emma hassan In what form do your tables exist in the computer? As matrices, perhaps? Could you upload a worksheet that contains this data?

@Markiyan Hirnyk Yes, much of the ListTools package is inefficient. Looking at showstat(ListTools:-Categorize), one can see that the time complexity is at least quadratic in the list length; possibly greater than quadratic because of the building of a sequence by iterative appending in statement 7:

result[j]:= result[j], i;

Since there's no need for us to actually construct the equivalence classes in this case, Statistics:-Tally is a better choice.

@Markiyan Hirnyk Yes, much of the ListTools package is inefficient. Looking at showstat(ListTools:-Categorize), one can see that the time complexity is at least quadratic in the list length; possibly greater than quadratic because of the building of a sequence by iterative appending in statement 7:

result[j]:= result[j], i;

Since there's no need for us to actually construct the equivalence classes in this case, Statistics:-Tally is a better choice.

@Joe Riel Thanks for the correction, Joe. I don't know where I got the idea that it was builtin. I took a look at showstat(subsindets). It is a masterpiece of simplicity! Just 15 short statements, 24 lines (including the code brackets end ..., etc.).

@Joe Riel Thanks for the correction, Joe. I don't know where I got the idea that it was builtin. I took a look at showstat(subsindets). It is a masterpiece of simplicity! Just 15 short statements, 24 lines (including the code brackets end ..., etc.).

How about first solving the problem in the plane z=1 (or, equivalently, z=0)? I don't know that there is such a solution, but I haven't looked.

Did that help? Did you figure out which series was correct, the alternating or the non-alternating?

Did that help? Did you figure out which series was correct, the alternating or the non-alternating?

Roughly how many equations?  I just need the order of magnitude. How many variables? Are the equations composed of rational expressions?

@J4James But what was the expected output in the example that you posted?

For example, what is "the desired output"?