I have currently a Maple session running with only one open worksheet.

The worksheet only contains an input line with the name "a" and an output line with the name "a".

The fan of my laptop is running full throttle and the task manager displays 10% CPU usage and a very high power usage (3 mserver.exe running, the process with the cpu load is javaw.exe. Suspending this process shuts down the fan).

After about an hour I decided to ask. While typing this post (in Firefox, probably unrelated) the CPU usage went down and the fan went quite. The total system CPU usage is now down to 2%.

Has anybody seen the same? What could have cause it? It's not the first time I observe this. Anything that I could check before restarting Maple? All on Windows 10 after system restart.

Update:

The thread that consumes cpu is called ucrtbase.dll!configthreadlocate

Starting Maplesim in parallel almost immediately turns off the fan while the displayed cpu load is still high but now variing.

I was not expecting to see step-by-step for this ode, but why does it give internal error instead of saying not supported? 

Am I doing something wrong in the call? Unfortunately, this Maple internal error can't be trapped at user level. Which means the whole program terminates also.

Download too_many_Levels_odesteps_oct_14_2024.mw

I have a procedure that I am trying to run that would be an improvement/more sophisticated way of solving a problem that I have previously solved. When I try and run my procedure I am getting an error, and from what I gather with the error is that there are some values when inserted into my procedure that cannot be evaluated. Just for context it is a procedure that contains numerical solutions to a system of DEs and and contains inequalities. 

I would like to know is there an easy method to figure out what values are giving me this error? 

Or a follow up, is there something wrong with my procedure that is giving me this error? I have included some commentary in my workshet as well to hopefully make everything clear. 

Thanks. 

Proc_Error.mw

I never really understood Intat. Help says 

"The intat command expresses an integral evaluated at a point; it is analogous to using the D command to express a derivative evaluated at a point."

But slope at a point is clear what it is and one can visualize it.

I do not understand what integral at single point means.

If one thinks of integration as area under the curve of the function, so what does area at single point mean? Should not integration (definite) always have lower and upper limits?

But my main question is not the above. I am sure there is a valid reason for Intat, otherwise it will not be in Maple.

But my quesiton is, in the context of solution to ode, can one replace result given using Intat by Int such that the lower limit starts from zero, and using same upper limit?

ie change Intat(...., a_ = something)  by Int( ... , a_ = 0 ... something) without changing the semantics or the correctness of the solution?

Because in  Intat, the lower limit is empty, and this always bothered me. At school the teacher says definite integration should have both lower and upper limits.

I tried it few places, and odetest verifies the solution of ode when using Intat or when using Int with lower limit zero:

Download intat_vs_int.mw

Is there a case you know, where solution of ode which has Intat, when replaced by Int with lower limit 0, will no longer verifies the ode?  I am not able to find one so far. But may be there is.
 

Update

fyi, I found case where it makes difference. Not for odetest, but when using value. When using Int(...,tau=0..upper) vs   Intat(....,tau=upper)

value was able to find the value when using Intat, but not when using Int (for this example). 

So I think I will just stick to Intat even though both verified the ode as valid solution as it is better to be able to find value for integral if possible. I knew there must be good reason why Intat was invented.

Download int_vs_intat_v2.mw

I have expression which can have many different functions  in it. Assume the expression is `+` type.

I do not know before what these function names are. 

Is there a way to make Maple collect on these functions automatically? Simplify does not do it. So if there is something like b*g(x)+g(x) in the expression, to simplify this to (1+b)*g(x) automatically?

I noticed if expression is   just b*g(x)+g(x) then simplify does give (1+b)*g(x) but once I add a new term, like 3+b*g(x)+g(x) then it no longer does it! which for me is very strange. I was expecting to get 3+(1+b)*g(x) 

Here is an example

Download simplification_oct_9_2024.mw

What do I need to do to get this output using another software

Ofcourse, I could go and add code to find the names of each function and then use collect. But it seems to me simplify should have done this automatically as the above shows. So I am wondering if there is an option I've overlooked which will do this more easily.

Maple 2024.1

In the rectangular Cartesian coordinate system, three straight lines gA, gB, gC are given, which are not all parallel to each other. Another straight line g and the points Oa, Ob, Oc on it are given. A triangle ABC is to be constructed, one of whose vertices lies on gA, gB or gC and the triangle sides a, b and c (or their extensions) each run through Oa, Ob or Oc.
We are looking for the coordinates of the vertices A, B, C.
In a purely constructive solution, the calculation can be omitted.

Hello,

I noticed that the Linearly Implicit Euler method (also known as the Semi-Implicit Euler method) is not available in Maple's built-in ODE solvers. This method is useful for stiff ODEs, where part of the function is treated implicitly (for the linear term) and part is treated explicitly (for the non-linear term).

I know that the Linearly Implicit Euler method is a specialized method that probably does not find enough widespread use to justify its inclusion as a standard feature in Maple, especially given Maple's focus on numerical methods such as Runge-Kutta methods and fully implicit methods for rigid equations.

I’m wondering:

1. Why isn’t this method included in Maple’s standard set of numerical solvers?
2. How can I implement this method in my own code in Maple to solve stiff ODEs?

Any guidance or examples of implementation would be greatly appreciated!

Thank you!

Linearly_Implicit_Method.pdf

Hello,

I need to order a set of polynomials based on a given ranking. For example:

F:=[F1,F2,F3,F4,F5,F6]:
F1 := x1*x4^2+x4^2-x1*x2*x4-x2*x4+x1*x2+3*x2;
F2 := x1*x4-x3-x1*x2;
F3 := x3*x4-2*x2^2-x1*x2-1;
F4 := x1*x3^2+x3^2-x1^2*x2*x3-x1*x2*x3+x1^3*x2+3*x1^2*x2;
F5 := -x3^2 + x1*x2*x3 -2*x1*x2^2-x1^2*x2-x1;
F6 := 2*x1*x2^2+2*x1^2*x2^2-2*x1^2*x2+x1^2+x1;

The order used to rank the polynomials is based on the variables in the following order: x1 < x2 < x3 < x4.

The ranking criteria are:

1. The first polynomial should be the one involving x4 with the lowest degree of nonlinearity in x4 and the fewest number of terms (in this case, F2).
2. The next polynomial should also involve x4, but with the lowest degree of nonlinearity and the next fewest number of terms and so on.
3. Once the polynomials in x4 are exhausted, the ranking continues similarly for the next variable x3, followed by x2, and finally x1.

How can I do this efficiently?

Obs.:If necessary, I can share my solution to the problem, though it's far from efficient.

Hello,

I am attempting to solve what appears to be a simple system of two ordinary differential equations (ODEs) (please find the attached file). However, I encountered an error message from Maple stating: "division by zero."

Could anyone suggest an approach to obtain a closed-form solution for this system?

Please note that the system includes two variables: S(t) and K(t). All other symbols represent positive parameters.

Thank you in advance for your assistance!

Best regards,

Dmitry

Download ODE.mw

A classic task from surveying that is unfortunately no longer taught in our GPS age and is worth remembering:

A hiker has lost his way and wants to know where he is. He has a map, a compass, paper, pen and calculator in his bag. From his position he sees three distant objects from left to right: a radio mast F, a chimney S and a church tower K. He also finds these objects on his map. Using his compass he aims at the three objects and measures the angles at which the distances FS and SK appear: angle for FS=alpha, angle for SK=beta. The hiker also manages to get the approximate coordinates of the three objects from the map to scale: F=(xf;yf), S=(xs;ys) and K=(xk;yk).
Question:
What are the hiker's coordinates?

Hello, I am having problem in solving the pde in the image using maple. Due to its nonlinear nature it has been solved for small value of v using first order perturbation technique and seperation of variable method into radial and angular part in many papers. I am having trouble in proceeding as Maple complains about Boundary/Initial condition.Please tell me if Maple can provide any help in improving existing solution or providing new solution? I can post the full solution procedure by the method i mentioned if needed.

Download Nonlinear_Elliptic_PDE_in_Spherical_Coordinate.mw

Just finished an exciting lecture for undergraduate students on Euler methods for solving ordinary differential equations (ODEs)! 📝 We explored the Euler method and the Improved Euler method (a.k.a. Heun's method) and discussed how these fundamental techniques work for approximating solutions to ODEs.

To make things practical and hands-on, I demonstrated how to implement both methods using Maple—a fantastic tool for experimenting with numerical methods. Seeing these concepts come to life with visualizations helps understand the pros and cons of each method.

The Euler method is the simplest numerical approach, where we approximate the solution by stepping along the slope given by the ODE. But there's a catch: using a large step size can lead to large errors that accumulate quickly, causing significant deviation from the real solution.

Plot Results:

• With a larger step size (h=0.5h = 0.5h=0.5), the solution tends to drift away significantly from the actual curve.
• Reducing the step size improves accuracy, but it also means more steps and more computation.

Next, we discussed the Improved Euler method, which is like Euler's smarter sibling. Instead of blindly following the initial slope, it:

1. Estimates the slope at the start.
2. Uses that slope to predict an intermediate value.
3. Then, it takes another slope at the intermediate point.
4. Averages these two slopes for a better approximation.

This technique makes a big difference in accuracy and stability, especially with larger step sizes.

Plot Results:

• Using the Improved Euler method, we found that even with a larger step size, the solution is smoother and closer to the true path.
• The average slope helps mitigate the inaccuracies that arise from only using the beginning point's derivative, effectively reducing the local error.

• The standard Euler method can produce solutions that oscillate or diverge, especially for larger step sizes.
• The Improved Euler method follows the actual trend of the solution more faithfully, even with fewer steps. This makes it a more efficient choice for balancing computational effort and accuracy.

• The Euler method is great for its simplicity but often requires very small step sizes to be accurate, leading to more computational effort.
• The Improved Euler method—which we implemented and visualized on Maple—proved to be more reliable and accurate, especially for larger step sizes.

It was amazing to see the students engage with these foundational methods, and implementing them on Maple brought a deeper understanding of numerical analysis and the challenges of solving differential equations.

Download Diff_equations.mw

Given a conventionally labeled triangle ABC with the two sides a=3 and b=4, c is not given. What is the side length of the largest inscribed square whose "base" lies on the triangle side c?

The usual ODE must be solved:
y´´*(y^3-y)+y´^2 *(y^2+1)=0
"Dangerous places" of the definition domain must be described: Where are the general solution y(x) and its derivatives continuous?

This is probably asked before but can't find it. 

After making a plot, then RIGHT-CLICKing on it, option menu comes up that allows one to modify the plot (like adding gridlines, or change the line style).

How does one find the Maple command after doing such changes, so one can use the command in the code?

Here is an example. I modified a little acers plot in this answer and added the points to the plot

eq:=-0.0004*x^2 - 2.7680*10^(-28)*x^12 - 2.1685*10^(-43)*x^18 - 1.3245*10^(-37)*x^16 - 1.6917*10^(-32)*x^14 + 0.7650 + 6.6773*10^(-18)*x^8 - 2.5543*10^(-23)*x^10 - 8.0002*10^(-13)*x^6 + 3.6079*10^(-8)*x^4 = 0:
the_roots:=fsolve(eq):	
the_roots:=map(X->[X,0],[the_roots]):
p1:=plot(lhs(eq),x=-210..210,size=[500,200]):
p2:=plot(the_roots,style=point, color=red, symbol=solidcircle, symbolsize=20):
plots:-display(p1,p2)

I was lazy to look up the grid option syntax. So right clicked on the plot and found option to add gridline. So said, great. And the above is the result.

But now I'd like to see the command used so I know where the grid option goes and how its syntax is. There does not seem to be option in the interface to display the Maple command used.

How would one find it?

Maple 2024.1 on windows 10