@pppc The differential order of the system of ODEs is 5 (order 3 in w(x) + order 2 in u(x)). So, solving the system for w(x) and u(x) without introducing extra constants requires 5 boundary conditions (BCs). If you want to use 6 BCs, you can force the value of one of the 5 constants that you already have.

@acer Thank you. Of course it's okay. Your input, Acer, is always more than welcome. And, in this case, the continuous= false is something that I needed to know about.

@pppc The x is what we call the independent variable---the variable with respect to which derivatives are taken. It's range is necessarily¹ constrained by the boundary points given in the problem specification. From the code in your Question, that would be 0..100.

The dependent variables are w and u--the unknown functions of the independent variable. They're the ones for which I'd like to know a very rough estimate of the maximum magnitude. Even better: The overall maximum of those functions and all of their derivatives used in the system. Just a single number covering all is needed.

As it has been posed, the system is solvable for diff(w(x), x) but not w(x) itself. To solve for w(x), I need one more initial condition. If you don't know, then we might as well make it w(0) = 0.

[1] We can extend the solution past the boundary points by starting an IVP solver at either boundary once the BVP solver gives us sufficient initial conditions.

@pppc Oh, the numbers are big. In that case, it'd also help if you told me a very rough estimate for the maximum magnitude of the dependent variables. Not taking this into account is one of those pitfalls that I was talking about.

I'm by no means an expert on the theoretical nature of BVPs. And that leaves me wondering, considering the high differential order of this system, Is it possible that there are multiple solutions? Is it possible for there to be complex solutions between the given boundary points? This would be a good time for an expert to speak up.

@ivanfanthony Yes, it's easy. But now I need one more parameter: an upper limit for t. Sure, it can go to infinity, but just for plotting, I need an upper limit. You'll still be able to exceed that limit on a numerical evaluation.

@pppc The command that puts sliders on the screen is Explore. See ?Explore. It's an amazing command; perhaps the best addition to Maple in years.

To start to learn how to solve BVPs numerically, look at ?dsolve,numeric and ?dsolve,numeric,BVP. There are many, many pitfalls during solving BVPs numerically. I think that this case will require expert help, like me (and there are a few other numeric BVP experts here on MaplePrimes). But I think that I could write a very basic Explore for this case in 2 minutes. I'll be able to do it later today. It'll not be possible to change Q(x) on the fly; that'll require manual input. In the meantime, it'd help if you'd specify acceptable ranges for the C__s.

@ivanfanthony It's no disturbance. I'm always happy to consider any question about my code.

The second argument of both Sum commands is l= 0..k, so all sums are starting at 0 and going to k (not k+1). However, there is no sum that is just Ss, as you pose above; there is nothing in my code that forms a sum like S(0)+ ... +S(5).

When you originally posted these equations, they appeared to me as difference equations because it looks like the independent variable is k; there is no other independent variable such as t or x. But, in consideration of your other Question thread, I see that each iterate S[k] is actually a real-valued function of a real variable, so should be styled as something like S[k](t). In light of that, the code above is irrelevant to your actual problem (and you should probably not waste time considering it further), although it does numerically solve the difference equations as they were posed. Also, it's now no surprise that the plotted solutions show no relation to your actual real-world problem. I'm guessing that it models the spread of a disease?

@nm My preference is that you leave the Question.

Try entering any computation, like "2+2". If you then lose the kernel, I'd suspect a firewall issue (like the error message says). Have you changed your firewall or Windows version recently? Are you on an institutional network that updates the firewall automatically?

@rahinui You must be using a very old version of Maple if the set order is session dependent.

@vv The straightforward dsolve/rkf45 solution that I got had a major periodic component with period approximately 10. I don't see how a series solution could possibly approximate that over the range 0..70 after only 3 iterations.

What difference would it make in the plot if the length were simply a positive number like 1 instead of your L?

@Ritti

To work on your version of Maple, try replacing the getdata command with

Smat:= op([1,3],sPlt);

and likewise for W.

Your ranges for x and t are much too large. Try using x= 0..1, t= 0..0.1. It seems to me that the x-range is restricted by the boundary conditions to be at most 0..1. I don't see how it can solve outside that boundary and why it doesn't raise an error for your x= 0..10. There's no upper limit for t, but the solution is boring if t gets much larger than 0.1.

The program's name is Maple, M-a-p-l-e. It's offensive to me when you people, Mr. riti, repeatedly misspell as "mapple" the name of the program that I love.

Could you post the original system of differential equations? I mean the equations from before the "homotopy analysis method" or any other partially applied solution technique has been used.

@ivanfanthony Post them as a separate Question. If they're substantially the same as this system, I'll try to get you to make changes to the code that I gave you. If they're substantially different, I'll probably do it. Either way, post everything that you know about the system right in the Question so that I don't need to ask a bunch of followup questions.