most of time is give me true my substittuetion but  a lot time i saw it is not make my substittuetion true and this time i figure out which author did   and outcome is what i am looking but when i do that is so different where is problem 

f-m.mw

In here i did try my best and my equation outcome are ok but is not same as author did i dont know why, beside this he try to use two ode for constructing  a new ode which find of one solution of this can be the third solution of ode!
 i have to use eq(5) for my orginal ode  but eq(5) contain f(x) and g(x) which by some assumption  and taking two other ode eq(6) and eq(7)  they construct new one which is eq(14) and by f(xi) and g(xi) have corelation with W(xi) which is third ode  as in eq(9) and eq(11) mentioned, i try to use the solution which author mentioned but is not give me solution of third ode by using corelation what is problem here? also in eq(21)  and eq(25) when thus parameter are satisfy must our odetest be zero

i will update two maple file which realted separatly for constructing  equations and other is for apply and satisfy the solution for ode!

F-p.mw

ode-17.mw

 a while ago there is a code for changing function from trig to hyperbolic and viceversa  but i can't find that code except changind xi=I*xi there is another one?

Download convert.mw

is been a while i work on it but i can't figure out where is problem and even my solution is so far from it when numerically i tested , i got same outcome as the paper did maybe is  long but it is same and maybe have some typical different but they are same , the problem in here is that which when i substitue is not my answer i don't know where is my mistake ?

pde-te.mw

f18.mw

f19.mw

Hello everyone
Dear experienced and expert friends
As a beginner, I would like to ask if any of my friends can guide me.
The following commands are related to Mathematica:

plots = Table[n = sValues[[i]];
   ParametricPlot[{1 - 2/n - 1.5/n^2 + (1.33 - 2/n) \[Gamma] - 
      0.0740741 (15 + 4*n) \[Gamma]^2, 
     12/n^2 + (16 \[Gamma])/n + (80 \[Gamma]^2)/9}, {\[Gamma], 0, 
     0.06}, PlotStyle -> colors[[i]], 
    PlotRange -> {{-10, 10}, {-10, 10}}], {i, Length[sValues]}];

Show[plots, Frame -> True, FrameLabel -> {"\!\(\*
StyleBox[SubscriptBox[\"n\", \"s\"],\nFontSize->16,\n\
FontColor->GrayLevel[0]]\)", "\!\(\*
StyleBox[\"r\",\nFontSize->16,\nFontColor->GrayLevel[0]]\)"}, 
 GridLinesStyle -> Black, PlotRange -> {{0.94, 1}, {0, 0.06}}, 
 PlotLegends -> 
  Placed[LineLegend[sValues, LegendLabel -> "s,w"], {0.5, 0.5}], 
 ImageSize -> 400]

I want to rewrite this process in Maple for my own functions.
I would be grateful if it is possible or if these commands are rewritten in a complete and executable form in Maple for me so that I can understand the working pattern. Or at least an equivalent command that can do this in Maple is introduced
Thank you all

What does Error, (in dsolve/numeric/bvp) bad index into Matrix mean?
Also, I'm trying to run it, it is slow, any suggestions?

restart;
with(Student[VectorCalculus]);
with(DynamicSystems);
with(DEtools);
with(PDEtools, ReducedForm, declare, diff_table, dsubs);
NULL;
 #Digits:= trunc(evalhf(Digits)); #generally a very efficient setting

# Here we solve a 1D problem in 3 regions. In each region, we have concentration and potential (c,phi) distributions,
# We first solve the unperturbed steady-state problem and then the linearized perturbation problem (which rely on the steady state).
# Each region is defined in x = 0..1, and the regions are connected by interface conditions that 
# connect (c1(1),phi1(1)) to (c2(0),phi2(0)) and (c2(1),phi2(1)) to (c3(0),phi3(0))

Q:=10;   omega:=100;     J0:= 0.01;   # parameters
                            Q := 10

                          omega := 100

                           J0 := 0.01

# The unperturbed steady-state

c1:=1-J0/2*x: 
c3:=1-J0/2*(x-1):  
c12:= eval(c1,x=1); 
c32 := eval(c3,x=0); 
S1:=sqrt(Q^2+4*c12^2): 
S3:=sqrt(Q^2+4*c32^2):  
c21:=eval((S1-Q)/2); 
c23:=eval((S3-Q)/2);  
I0:=fsolve(Q*i0/2/J0*ln((J0*S1-Q*i0)/(J0*S3-Q*i0))=(J0-S1+S3)/2,i0);  
V:=(I0/J0+1)*ln(c32/c12)+ln((c21+Q)/(c23+Q))+(J0+2*c23-2*c21)/Q; # the potential drop across the system 
c2:=solve(y-c21+Q*I0/2/J0*ln((Q*I0-Q*J0-2*J0*y)/(Q*I0-Q*J0-2*J0*c21))=-J0/2*x,y):  
phi1:=I0/J0*ln(c1)+V: 
phi3:=I0/J0*ln(c3): 
dphi1:=diff(phi1,x); 
dphi3:=diff(phi3,x); 
phi21:=I0/J0*ln(c12)+V-0.5*ln((c21+Q)/c21); 
phi2:=(2*c21-2*c2+Q*phi21-J0*x)/Q: 
dphi2:=diff(phi2,x); 
dphi12 := eval(dphi1, x=1); 
dphi21 := eval(dphi2, x=0); 
dphi23 := eval(dphi2, x=1); 
dphi32 := eval(dphi3, x=0); 
INT1 := int(1/(2*c1), x = 0 .. 1); 
INT2 := int(1/(2*c2 + Q), x = 0 .. 1); 
INT3 := int(1/(2*c3), x = 0 .. 1); 
INT := INT1 + INT2 + INT3;
                      c12 := 0.9950000000

                       c32 := 1.005000000

                      c21 := 0.09804129000

                      c23 := 0.1000024500

                      I0 := 0.01419804328

                       V := 0.02539628566

                              0.007099021640   
                dphi1 := - --------------------
                           1 - 0.005000000000 x

                              0.007099021640        
           dphi3 := - ------------------------------
                      1.005000000 - 0.005000000000 x

                     phi21 := -2.299074561

dphi2 := (0.001000000000 LambertW(-0.2818670588 exp(-0.2818670588

   - 0.0007043224058 x)))/(1

   + LambertW(-0.2818670588 exp(-0.2818670588 - 0.0007043224058 x)

  )) - 0.001000000000

                   dphi12 := -0.007134695118

                   dphi21 := -0.001392499832

                   dphi23 := -0.001391964358

                   dphi32 := -0.007063703124

                      INT1 := 0.5012541824

                     INT2 := 0.09805801917

                      INT3 := 0.4987541511

                       INT := 1.098066353

sys1 := {
-omega*C11(x)+diff(diff(C12(x), x), x)=0,
omega*C12(x)+diff(diff(C11(x), x), x) = 0,
-omega*C21(x)+diff(diff(C22(x), x)+(c2*sigma2-C22(x)*dphi2*Q)/(2*c2+Q), x) =0,
 omega*C22(x)+diff(diff(C21(x), x)+(c2*sigma1-C21(x)*dphi2*Q)/(2*c2+Q), x) = 0,
-omega*C31(x)+diff(diff(C32(x), x), x)=0,
omega*C32(x)+diff(diff(C31(x), x), x) = 0
}:

sys2 := {
diff(FA1(x), x) = C11(x)*dphi1/c1,
diff(FA2(x), x) = C21(x)*dphi2/(c2+Q/2),
diff(FA3(x), x) = C31(x)*dphi3/c3,
diff(FB1(x), x) = C12(x)*dphi1/c1,
diff(FB2(x), x) = C22(x)*dphi2/(c2+Q/2),
diff(FB3(x), x) = C32(x)*dphi3/c3
}: 

Bc := {
C11(0) = 0, C12(0) = 0,  C31(1) = 0, C32(1) = 0,
FA1(0) = 0, FB1(0) = 0,  FA3(1) = 0, FB3(1) = 0, 

2*C11(1)/c12 = C21(0)/(c21+Q)+C21(0)/c21, 
2*C12(1)/c12 = C22(0)/(c21+Q)+C22(0)/c21,
C21(1)/(c23+Q)+C21(1)/c23 = 2*C31(0)/c32,
C22(1)/(c23+Q)+C22(1)/c23 = 2*C32(0)/c32,

D(C11)(1)+dphi12*C11(1)-sigma1/2-c12*D(FA1)(1) = D(C21)(0)+dphi21*C21(0)-(c21+Q)*sigma1/(2*c21+Q)-(c21+Q)*D(FA2)(0),
D(C12)(1)+dphi12*C12(1)-sigma2/2-c12*D(FB1)(1) = D(C22)(0)+dphi21*C22(0)-(c21+Q)*sigma2/(2*c21+Q)-(c21+Q)*D(FB2)(0),
D(C11)(1)-dphi12*C11(1)+sigma1/2+c12*D(FA1)(1) = D(C21)(0)-dphi21*C21(0)+c21*sigma1/(2*c21+Q)+c21*D(FA2)(0),
D(C12)(1)-dphi12*C12(1)+sigma2/2+c12*D(FB1)(1) = D(C22)(0)-dphi21*C22(0)+c21*sigma2/(2*c21+Q)+c21*D(FB2)(0),

D(C31)(0)+dphi32*C31(0)-sigma1/2-c32*D(FA3)(0) = D(C21)(1)+dphi23*C21(1)-(c23+Q)*sigma1/(2*c23+Q)-(c23+Q)*D(FA2)(1),
D(C32)(0)+dphi32*C32(0)-sigma2/2-c32*D(FB3)(0) = D(C22)(1)+dphi23*C22(1)-(c23+Q)*sigma2/(2*c23+Q)-(c23+Q)*D(FB2)(1),
D(C31)(0)-dphi32*C31(0)+sigma1/2+c32*D(FA3)(0) = D(C21)(1)-dphi23*C21(1)+c23*sigma1/(2*c23+Q)+c23*D(FA2)(1),
D(C32)(0)-dphi32*C32(0)+sigma2/2+c32*D(FB3)(0) = D(C22)(1)-dphi23*C22(1)+c23*sigma2/(2*c23+Q)+c23*D(FB2)(1)
}:
 
 

all_sys := sys1 union sys2 union Bc:
sol1 := dsolve(all_sys, initmesh = 100, maxmesh = 15000, numeric, method = bvp[midrich], output = listprocedure):
#(all_sys, numeric, method = bvp[midrich]);

Error, (in dsolve/numeric/bvp) bad index into Matrix

I'm looking for the general solution to the attached differential equation. Maple doesn't provide it. What am I doing wrong?

Download testdgl5.mw

i did try and even replace the function w(t) by anotehr thing but is not working  how i can find that and make be answer of my pde?

k1.mw

a million time i try to figure out how i can get this plot ? why my graph  in countor is not same the 3D plot? where is problem?

Bgraph1.mw

In this kind of contour plot i have two line but when i change time variable t just contour of one line wil move the other is not do any movement and is stop how i can  make the second plot one second line move too? also there is any way for ploting this kind any other option?

line-2-done.mw

It is possible to perform the simplest QFT calculations with second quantization, in Maple? Bosons in a box. See attached example. bosons_in_a_box.mw

Sure any general purpose programming language is capable of performing this task with enough effort. What I am interested in is if the physics tools has a standard way of dealing with these calculations. The general impedement when attempting the calculation is that integrations are perfomed by replacements with delta functions or kronecker delta functions, and its not clear how to force the Maple Physics package to recognize this or if that's possible. Part of the problem is that integrations in maple are defined in one dimension at a time where as in QFT the integration element is almost always atleast three dimensional, d^3x or dxdydzy, the later of which can get extremely cumbersome with even a small number of fields under consideration. I don't find much of what I am refering to mentioned in the help pages and I doubt these types of QFT calculations are possible to perform in Maple without addressing these issues.

bosons_in_a_box.mw

i don't  know  why my graph make a problem and what is issue i did plot  but this time make issue for me which i don't know where is problem there is anyone which can help and even modified the plot?

explore-chaotic.mw

In thus manuscript i got some reviewer comment which is asked to simplify this expresion and there is a lot of them maybe if i do by hand i  made a mistake becuase a lot of variable so how i can fix this issue and make thus square root are very simple as they demand

Download simplify.mw

what is problem in here

Download remove.mw

i want plot a system of differential equation and do phaseportrait i did but when i want make it a little bit more clear and colorfull like rainbow when i find the C.Q i don't know how set the option for ploting?

e1.mw