Is there a trick to make Maple give same result below when using eval and limit?  

Attached worksheet. This comes in context of solving ode  using Laplace. Initial conditions are at zero. And need to solve for the constant of integration. 

It works when using eval, since Dirac(t) becomes Dirac(0), but when using Limit, Dirac(t) becomes zero and the _C1 is lost. I was wondering if limit should also return Dirac(0) like eval?

Download dirac_limit_dec_13_2024.mw

Some of the calculations mentioned here can be done in alternative programming languages, such as Python, C, and so on. However, I would like to reproduce exactly these graphs using Maple (without the need for programming commands, such as "if", "while", among others).

In the work I am trying to reproduce, we have "The evaluation of the influence of the inclusion of the broadband behavior of grounding systems in EMT-type programs in the evaluation of transients resulting from direct lightning strikes on transmission lines. The behavior of the grounding frequency is determined using an accurate electromagnetic model and included in the EMTP/ATP by means of an equivalent circuit derived from the Vector Fitting technique. In addition, the impact of the frequency dependence of soil parameters on the lightning performance of transmission lines is addressed." This may seem somewhat disconnected from reality for many, since it is a problem involving electrical engineering optimization.

Could someone help me reproduce these calculations? I have made little significant progress.

If you want to access the reference accounts, I'll send you the PDF

schroeder2017 [link to copyrighted material replaced by moderator]

Hello Dear Maple Users and Experts

I am running this code for N=3, but fsoolve can not work and did not give me any output. Could you help me how can I get the result?

Actually, I got the result for N=2. Exact solution is a[0]=0, a[1]=1, a[2]=1, b[1]^2=sqrt(2) and b[1]^2+b[2]^2=sqrt(3). But, for N=3, I can not receive any results from fsolve

Here is my code

restart;
Digits := 20;
L := 1;
N := 3;
alpha := 1;
xexact := t -> t^sqrt(2) + t^sqrt(3);
f := simplify(fracdiff(t^sqrt(2), t, alpha)) + simplify(fracdiff(t^sqrt(3), t, alpha));
f := unapply(f, t);
xapp := a[0] + sum(a[j]*t^sum(b[i]^2, i = 1 .. j), j = 1 .. N);
xapp := unapply(xapp, t);
xfrac := sum(a[jj]*simplify(GAMMA(sum(b[ii]^2, ii = 1 .. jj) + 1)/GAMMA(sum(b[ii]^2, ii = 1 .. jj) + 1 - alpha))*t^(sum(b[ii]^2, ii = 1 .. jj) - alpha), jj = 1 .. N);
xfrac := unapply(xfrac, t);
xfrac1 := sum(a[jj]*simplify(sum(b[ii]^2, ii = 1 .. jj)^(alpha + 1)/(sum(b[ii]^2, ii = 1 .. jj) - alpha))*t^(sum(b[ii]^2, ii = 1 .. jj) - alpha), jj = 1 .. N);
xfrac1 := unapply(xfrac1, t);
S1 := {seq(evalf(xfrac(k/(2*N)*L)) - evalf(f(k/(2*N)*L)) = 0, k = 1 .. 2*N)};
S2 := {xapp(0) = 0};
S := S1 union S2;
sol := fsolve(S);

I'm evaulating Maple Flow and wondered if any Mathcad users have transferred to Maple Flow?

What are the pros/cons of Maple Flow? It's different to what I'm used to so I need to spend time learning. But I'm liking what I see so far.

Hi,
How can I simplify this relation(See uploaded .mw file)?
For example, the second term is simplified as: 

deltae*(1-phi0/(kappa-3/2))^(-kappa+1/2)+(1/2)*deltab*(1-sqrt(2)*sqrt(1/(m*ub^2))*sqrt(-phi0));

di1.mw

In Latest Maple 2024.2, I found that when doing z:=%  where % is result on integration, causes internal error 

          Error, unexpected result from Typesetting

But when the interface is set to standard, no such error.

This not only happen in worksheet, but also when code is run in command line!

Worksheet below.

Download extended_interface_causes_internal_bug_dec_13_2024.mw

ps. also reported to Maple support

I was rejected because the editor said my equation is too long. My question is: Is there a way to rewrite the equation in a more concise form? Additionally, is there a package in Maple that allows for automatic simplification or collection of terms without using specific commands? Any suggestions for addressing this issue would be appreciated.

Download coment.mw

hi,

I would like help with 2 questions regarding complex plots and Euler's formula:

- I'm trying to plot a complex (simple) plot in Maple Flow (2024.2) but got into a problem:

does anyone would know how to fix/solve it?

- how could an complex exponential function be expanded with Euler's formula

Thanks very much in advance.

Where can I found details about Statistics:-Sample(..., method=envelope).

It would be nice to have a link to a description of the envelope method Sample uses.
For instance does it share some features of the Cuba library for numeric integration? Does it use the same envelope method evalf/Int(..., method=_CubaSuave)) uses?

Thanks in advance.

I'm having trouble solving this system of differential equations. I haven't solved systems of differential equations before but i tried defining the system and then using dsolve, but it couldn't solve all the equations.

Hope you can help.

Download System_Of_Differential_Equations.mw

I'm trying to transform a partial differential equation (PDE) into an ordinary differential equation (ODE) as demonstrated in the paper. However, I find some steps confusing and difficult to follow. The process often feels chaotic, and managing the complexity of the equations is overwhelming. Could you suggest an effective and systematic method to handle such transformations more easily?

Download transform-pde-to-ode-hard_example.mw

I have expected the opposite. Is exp already optimised that hardware floats do not make sense or does the conversion of the argument to hardware floast eats up all the benefit of using hardware floats?

restart;
CodeTools:-Usage( for i from 1 to 100 by 0.1 do exp(i) end do):
CodeTools:-Usage( for i from 1 to 100 by 0.1 do (evalhf@exp)(i) end do):
memory used=1.54MiB, alloc change=0 bytes, cpu time=16.00ms, real time=15.00ms, gc time=0ns
memory used=5.88MiB, alloc change=32.00MiB, cpu time=31.00ms, real time=33.00ms, gc time=0ns

Is there a way to determine how we can construct a system of equations from this complex PDE? Also, moderator, you mentioned I could create a new question using the branch option, but you deleted my previous question, which led me to delete my earlier post. don't delete this one.

Download PDE-Hard.mw

The output  means that there is no real solution, but clearly, both and  satisfy the original equation: 

So, why does `solve` lose the real solutions without any warning messages? 
Code: 

restart;
eq := 9*(x^2 + 2*cos(x)) = Pi^2 + 9;
RealDomain:-solve(eq, [x]);
                               []

:-solve({eq, x >= 0}, [x]); # as (lhs - rhs)(eq) is an even function 
                               []

this equation will be solve by changing variable but when  i found the function and substitute the ODE is not zero where  is mistake?

Download problem.mw