Dear Users!

I hope everyone is fine here. In the attached file I have solved a partial differential equation using the finite difference method for different mesh in spatial directions (i.e., for different Mx). I want to compute the time and memory to compute the solution against each Mx and want to plot it. Kindly help me how to compute the time and memory for each value of Mx.

TIME.mw

I shall be waiting. Thanks in advance. 

I want a maple code to solve the caputo fabrizio differential equations using Runge Kutta method with implicit functions and impulsive conditions in maple. Is there any code structure for that. 

restart;
with(Student[NumericalAnalysis]);
with(plots);
with(DEtools);
f := proc(u, r) local res; res := 1/25*r^2 + (sin(u(r)) + sin(diff(u(r), [r $ 1/5])))/(r^2 + 47); return res; end proc;

RK4 := proc(f, u0, r0, h, n) local u, r, i, k1, k2, k3, k4; u := Vector(n + 1); r := Vector(n + 1); u[1] := u0; r[1] := r0; for i to n do k1 := f(u[i], t[i]); k2 := f(u[i] + 1/2*h*k1, r[i] + 1/2*h); k3 := f(u[i] + 1/2*h*k2, r[i] + 1/2*h); k4 := f(u[i] + h*k3, r[i] + h); u[i + 1] := u[i] + 1/6*h*(k1 + 2*k2 + 2*k3 + k4); r[i + 1] := r[i] + h; end do; return [u, r]; end proc;
RK4 := proc (f, u0, r0, h, n) local u, r, i, k1, k2, k3, k4; u 

   := Vector(n+1); r := Vector(n+1); u[1] := u0; r[1] := r0; 

   for i to n do k1 := f(u[i], t[i]); k2 := f(u[i]+(1/2)*h*k1, 

   r[i]+(1/2)*h); k3 := f(u[i]+(1/2)*h*k2, r[i]+(1/2)*h); k4 := 

   f(u[i]+h*k3, r[i]+h); u[i+1] := u[i]+(1/6)*h*(k1+2*k2+2*k3+k4\

  ); r[i+1] := r[i]+h end do; return [u, r] end proc

u0 := cos(abs(0.9))/15;
                      u0 := 0.04144066455

r0 := 0;
                            r0 := 0

h := 0.1;
                            h := 0.1

n := 100;
                            n := 100

solution := RK4(f, u0, r0, h, n)

u := solution[1];
r := solution[2];
plot(u, r, style = line, color = blue, labels = ["Time (r)", "Solution (u)"]);
 is this correct to solve the implicit fractional differential equations using 4th order Runge-Kutta Method. will fsolve command  solve the fractional differential equations ?

Hello
i am using maple 2023 and the physics package and have the following question:
I want to define a gauge-  plus coordinate covariant derivative i.e.
assuming i,j,k are SO(3) indices and greek indices describe 4-dim space-time (not necessary flat)
i need the following derivative:

D_sigma F_i _rho _lambda = nabla_sigma F_i _rho _lambda + epsilon_i ^j ^k  A_j_sigma  F_k~rho~lambda
with _ meaning lower indices and ^ upper indices and nabla the convenient coordinate covariant derivative of general relativity.
F is a tensor objekt with 2 space time indices and 1 so(3) indices (e.g. Yang Mills field strength) and A is the so(3)gauge potential
How can i define this Differentialoperator with the physics package.
I.e. i want to work with SO(3) Yang-Mills Fields in curved space time and need this generalized Differentialoperator
thanks for helping. I hope its clear from this ascii text in the screen
regards Michael

How should optional input parameters be handled for procedures. The example has three optional inputs 

vars:=[x,y]   ,  clr:="b"   and prnt:="y"  . if one wants to change prnt to"n", vars and clr values must be entered.

{vars:=[x,y]  } , { clr:="b" }  and{ prnt:="y"}  this is a good method because one just enteres prnt="n".  But have to remember the input parameter name prnt.

I have a 3rd option, but it is to complicated and probably unreliable to use in practice.  and with more than 3 optional inputs too difficult to code.

I am wondering  are the other approaches and what is the prefered methodology. I have about 30+ procedures to apply this to in a package.

Edit:-  I can change the prnt to boolean true, false instead of "y" , "n".  That would make the all the optional inputs different types.

In Test1 its should be vars::list:=[x,y] not vars::{list , `string`}:=[x,y]

Download Q_2024-02-25_Test_proc_Args.mw

ow to get plot for the exact solution of a piecewise function and i need the correct plot which has curve started at y-axis (0.5) and goes till 2?

Hello,
I am a beginner on Maple and I am working on approximate solutions of partial differential equations.
After finding the approximate solution I wanted to compare both the plots (The exact solution and the approximate one), is here any tool or command that allows me to do so ?

Thanks in Advance !

I want to know the change of the web during the web handling process, so I attached the probe, and it shows the checkboxes to observe the velocity and tension values as shown in the picture, but there are 3 additional checkboxes like Force - T2 / real - e / real - e2, what does this mean?

Can I link my MapleCloud application to the Application Center?

Several years ago I uploaded an installable workbook application for Clifford Algebra to the public maplecloud following the guidelines and formats set down in maple help. My intention was to make the application available in the application center, but I just noticed that a package uploaded to MapleCloud is not  available for searching in the Application Center. Unfortunately,the Maple Cloud site for public packages is a mess. One cannot readily browse the applications there like in the application center.

The submissions page for the application center is not helpful in this case. It seems to assume submissions will take the form of maple documents/ worksheets rather than applications written in a workbook). I could not navigate to the Maple Cloud to drop a link to my package using the submission form, but it should be possible to link the the package already installed on the MapleCloud to the Cloud? (Because I is easier to update the MapleCloud package and it can be installed by opening from the Cloud).

Applying Maple 2023's dsolve to the ODE shown below yields the solution y(t)=0 which is obviously incorrect.  Maple 2021 and earlier used to give a nonzero (albeit not very useful) answer.

Download dsolve-bug.mw

I have a problem. Maple wants to create and a palette, I can add content and icons to the palette, but as soon as I restart Maple, the palette content has disappeared and says that Maple cannot find the added icons.

I have used the method described in Maple Help.

Is there anyone who can help?

Kind regards

Dear sir ,

I have implemented Dsolve method the code was executed, but i need to apply Kellor Box method to solve the ODES 

Please can any one help how to implement? 

because there is no post regarding the Kellor box method. 

Download kellor_box_method.mw

Is there an equivalent to Pivot Table in Excel?
I'm working on some investing data, and am using Maple to gather information from various sources and using DataFrame to combine all the data. I could export the dataframe and open in Excel or other spreadsheet and use the Pivot table to summarize the data, but is there an easy way to do all of it in Maple?

Thanks

Good evening,could you please help me to find the values of Phi[2],Phi[3],Phi[4],....

The right hand side of the for loop is the equation i need.Is this maple code correct.

rps1.mw

I have doubts as to whether this is possible, but I would like to ask anyway.

For example, can

`*`(`+`(a, b), c);
                           c (a + b)

be written with composed procedures (`*`@`+`) and somehow grouped arguments (a,b) for `+` and (a+b,c) for `*`.

So far I have only come across composed procedures in parethesis applied to one expression in parenthesis.

Since the second pair of parenthesis does a function application to everything what is inside the parenthesis it seems impossible that the right most procedure is only applied to a sub-term of the expression first.

If the answer to my question is no, I want to aks a related question:

Is it possible to separate procedures calls from arguments? So, in a first part of a statement I have a sequence (or a list or a composed function) of procedures/operators and in the second part a sequence of arguments instead of a nested construct of procedure calls?