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

I want to find the formula for seq: 

För example 

{0,4,16,36,64,100,..}

{0,3,6,11,18,27.38,...}

How do i revers i backword fo get arithmetic sequence formula. I now the answare but want to learn how it's done in maple. I tried the app but i was not able to solve it. I have read the help and it looks like you have to use rsolve. Does anyboy has a sample to do not is trail and error. 

Download bug-in-plot.mw

Hi.

why in eq1 some parameters such as beta 1, Q110,... are not placed (They defined before eq1 !!!!)

Thanks

TRASH.mw

When I use IdentifySmallGroup(DihedralGroup(4)), I will get result 8,3. Then I know DihedralGroup(4) is SmallGroup(8, 3) actually. But I will get different result when I use it in IsTransitive:

IsTransitive(DihedralGroup(4), [1, 2, 3, 4])

true

IsTransitive(SmallGroup(8, 3), [1, 2, 3, 4])

false

How to rectify this error.

NF-1.mw

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

Cong:=proc(n)
 local  a,b,An,Bn,Cn,Dn:
if n mod 2 = 1    
An:=0:     Bn:=0:    
for a  from (round(-sqrt(n/(2)))) to round(sqrt(n/(2)) )
do:           
for b  from (round(-sqrt(n)) )to round(sqrt(n) )do :               
if (sqrt(n-2*a^(2)-b^(2)) )/(32)isInteger                      
then An:=An+1                
elif (sqrt(n-2*a^(2)-b^(2)) )/(8) isInteger                      
then Bn:=Bn+1  fi:          
od:  od:
 if 2*An=Bn  
 return(True)  else  return(False)
fi: else if n mod 2 = 0 : 
Cn:=0:  Dn:=0:      
for a  from (round(-sqrt(n/(8)))) to round(sqrt(n/(8)) )
do :          
 for b  from (round(-sqrt(n/(2)))) to round(sqrt(n/(2))) do:                 
f (sqrt(n/(2)-4*a^(2)-b^(2)) )/(32)isInteger                      
then Cn:=Cn+1                
elif (sqrt(n/(2)-4*a^(2)-b^(2)) )/(8) isInteger
then Dn:=Dn+1 fi: od:  od:  
if 2*Cn=Dn:   
return(True)  else  return(False)fi:  
end:  

Why do I get this messge : Error, unterminated procedure. Thank you.

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?

Using textplot  is there anything that can be done to to increase the offest of align? I would like to raise  P3 at top of graph up a bit and S3 down. they are {centre, above} and {centre,below}. I know I can tie them to a different point  coordinate to begin with but that is messy to control inside a procedure.

How to compare the magnitude (the absolute value, ignoring the sign) of two multi-parameter functions f_1 and f_2?

Note that all my parameters can only take stricly positive values. Specifically, I want to know the ranges of parameter values for which f_1 > f_2, f_1 < f_2, and f_1 = f_2. Is solve(f_1 > f_2) etc. the best way to do this? If so, how to specify solve() so that it incorporates all three (>,<,=) comparisons and do not ignore the strict positivity assumption? Is there any other command other than solve()?   

Example with only two parameters sigma__v and sigma__d:

Download parametric_comparison.mw

Note that f_1 depends only on sigma__d but f_2 depends on both sigma__v and sigma__d. Of course I can directly plot the two curves in 3d in this simple case, but I am looking for a systematic way to do parametric comparisons so that I don't have to "eyeball" the threshold values (if any exist). Most importantly, I can't plot at all once my functions depend on more than two parameters.

 Thanks.

EDIT: perhaps "variables" is a better word than "parameters" here.