dear all,

I have a problem when I try to find points on boundary of the surface.

the surface ploted from a matrix as follow:

please help me to generate a bondary curve of this surface.

Thanks

Having difficulties solving pde. Below is the problem and its not plotting. Anyone with useful informations. Please

restart;
with(PDEtools, casesplit, declare);
with(DEtools, gensys);
with(Physics);

PDE := diff(theta(x, t), x, x)+beta*theta(x, t)*(diff(theta(x, t), x, x))+beta*((diff(theta(x, t), x))^2)-M^2*theta(x, t)-S[h]*(theta(x, t)^2)+M^2*G*(1+E*theta(x, t))-P[e]*(diff(theta(x, t), x)) = diff(theta(x, t), t);
/ d  / d             \\
|--- |--- theta(x, t)||
\ dx \ dx            //

                      / d  / d             \\
   + beta theta(x, t) |--- |--- theta(x, t)||
                      \ dx \ dx            //

                           2                                     
          / d             \     2                               2
   + beta |--- theta(x, t)|  - M  theta(x, t) - S[h] theta(x, t) 
          \ dx            /                                      

      2                              / d             \    d  
   + M  G (1 + E theta(x, t)) - P[e] |--- theta(x, t)| = --- 
                                     \ dx            /    dt 

  theta(x, t)
BC := theta(x, 0) = 0, Dt(theta(0, t)) = 0, theta(1, t) = 1;
     theta(x, 0) = 0, Dt(theta(0, t)) = 0, theta(1, t) = 1
Codes := [beta = .1, M = .1, S[h] = .1, G = .1, P[e] = .1, E = .1];
S1 := pdsolve({BC, subs(Codes, PDE)});
PDEplot(S1, [[t, theta(x, t)], [x, theta(x, t)]], t = 0 .. 1, x = 0 .. 1, iterations = 2, numchar = [10, 10], stepsize = 0.5e-1, numsteps = [-5, 5]);
   PDEplot([[t, theta(x, t)], [x, theta(x, t)]], t = 0 .. 1, 

     x = 0 .. 1, iterations = 2, numchar = [10, 10], 

     stepsize = 0.05, numsteps = [-5, 5])

Hi

I have two equations as follows:

The goal is finding the parameter 'phi'. This parameter is a positive real numeric constant.

I uploaded two files that they are included two methods to solve the problem.

1.mw

2.mw

Is method in the first file mathematically logical? If it is a correct method, why the command fsolve dosent work?

In file 2, we have 2 equations with further indeterminantes. The constant 'phi' must be minimum possible amount. How we can use the commands like the Minimize in Optimization? Please hint me.

Moreover, if there is a method to solve this problem please help me to know.

Thank you very much 

I am coding a big module to solving my project : analyze function in math, but when I compile my module maple return "Error," but it doesn't tell me what error happened.

I check the maple help and it said:" If no msgString is given, error raises the most recently occurring exception" but I have no exception before. 

This is the pic of that error.

Thank for your help.

Hi,

I have three simultaneous equations  with three unknown variables (E, W, T). When I solve these  simultaneous equations with fsolve command without specifying any range for variables, I don't get desirable root ( equation sol4 in maple worksheet- {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}). For this problem, I know the correct root {E = 2843.916504, T = .2782913990, W = 5344.844134} beforehand which maximize the objective function TP (equation sol8 in maple worksheet) and when I specify the narrow range of variables around the already known correct root in the fsolve command, then I get correct root ( equation sol5 in maple worksheet). If I don't know the actual answer (correct roots of the simultaneous equation) beforehand, How  could I get the correct root with fsolve command because it is very tedious work to specify different range in fsolve command repetitively to solve it by trial and error.

I also tried Direct Search method as suggested in this forum  but DirectSearch is also not able to provide the correct root (equation sol6 in maple worksheet). If I specify the narrow range around known root in direct search method ( equation sol6a in maple worksheet), then it would provide close to optimal root but if I don't know the correct root beforehand, then I couldn't specify the narrow range of variables, then how can I get correct root through direct search command.

Equation sol10 in maple worksheet  (objective function value at correct root) confirms that {E = 2843.916504, T = .2782913990, W = 5344.844134} is the correct root because it provide the value of objective function (TP) equal to 78285.85621 as opposed to negative value (TP value -12.53348074 in equation sol9)  produced by incorrect root  {E = 0.1007672475e-2, T = .7969434549, W = 0.1937272759e-2}).

Is there any method which would provide all the roots of these simultaneous equations which also include correct root. Maple worksheet is attached.

I am trying fsolve and direct search method with known root so that I could get the proper procedure to get the correct root which I can apply to another problem (set of similar simultaneous equations) for which I don't know correct root beforehand.

Thanks for your anticipated help.fsolve_question.mw

Dear Maple users,

I have very interesting problem with evaluating of only symbolic equations.

The problem is: (In document mode)
When I try to evaluate all numeric values for example typing 1+2 and press Enter it successfuly evaluates 3.
But when I try to evaluate symbolic values for example x + y nothing happens.

I tried lots of things to solve this, but no luck.
Shortly if the equation contains only numbers it evaluates successfuly.
And if the equation contains one or more symbolic variables like (x, y, z, variable1, test1), it does nothing.

What could be the problem?
 

(Because of this problem I cannot use the document mode, so I'm using the worksheet mode. Worksheet mode works good, but sometimes it is not calculating like document mode)

System is Windows 7 x64
Maple 2016
8 x 3.50GHz Xeon CPU
128 GB RAM
Windows Language is Turkish, (I tried with also USA English, but no luck either)
Keyboard is Turkish TR, (I tried with also US English, but no luck either)

Hello everyone.

Please can I meet with Computational or/and Numerical anlysts that have worked or working on the algorihms particularly (Runge Kutta Nystrom, Block multistep methods including hybrid and Block Boundaru Value methods) for the solution of both IVP and BVP.

I will appreciante if I can learn from them and possibly collaborate with them. Thank you in anticipation of your positive response.

Please I am having problem with this code particularly the last subroutine

#subroutine 1

restart;
Digits:=30:

f:=proc(n)
    -25*y[n]+12*cos(x[n]):
end proc:

#subroutine 2

e1:=y[n+4] = -y[n]+2*y[n+2]+((1/15)*h^2+(2/945)*h^2*u^2+(1/56700)*h^2*u^4-(1/415800)*h^2*u^6-(167/833976000)*h^2*u^8-(2633/245188944000)*h^2*u^10-(2671/5557616064000)*h^2*u^12-(257857/13304932857216000)*h^2*u^14-(3073333/4215002729166028800)*h^2*u^16)*f(n)+((16/15)*h^2-(8/945)*h^2*u^2-(1/14175)*h^2*u^4+(1/103950)*h^2*u^6+(167/208494000)*h^2*u^8+(2633/61297236000)*h^2*u^10+(2671/1389404016000)*h^2*u^12+(257857/3326233214304000)*h^2*u^14+(3073333/1053750682291507200)*h^2*u^16)*f(n+1)+((26/15)*h^2+(4/315)*h^2*u^2+(1/9450)*h^2*u^4-(1/69300)*h^2*u^6-(167/138996000)*h^2*u^8-(2633/40864824000)*h^2*u^10-(2671/926269344000)*h^2*u^12-(257857/2217488809536000)*h^2*u^14-(3073333/702500454861004800)*h^2*u^16)*f(n+2)+((16/15)*h^2-(8/945)*h^2*u^2-(1/14175)*h^2*u^4+(1/103950)*h^2*u^6+(167/208494000)*h^2*u^8+(2633/61297236000)*h^2*u^10+(2671/1389404016000)*h^2*u^12+(257857/3326233214304000)*h^2*u^14+(3073333/1053750682291507200)*h^2*u^16)*f(n+3)+((1/15)*h^2+(2/945)*h^2*u^2+(1/56700)*h^2*u^4-(1/415800)*h^2*u^6-(167/833976000)*h^2*u^8-(2633/245188944000)*h^2*u^10-(2671/5557616064000)*h^2*u^12-(257857/13304932857216000)*h^2*u^14-(3073333/4215002729166028800)*h^2*u^16)*f(n+4):

e2:=y[n+3] = -y[n+1]+2*y[n+2]+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(n)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(n+1)+((97/120)*h^2-(31/10080)*h^2*u^2-(67/302400)*h^2*u^4-(109/8870400)*h^2*u^6-(18127/31135104000)*h^2*u^8-(64931/2615348736000)*h^2*u^10-(9701/9880206336000)*h^2*u^12-(20832397/567677135241216000)*h^2*u^14-(11349439/8646159444443136000)*h^2*u^16)*f(n+2)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(n+3)+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(n+4):

e3:=h*delta[n] = (-149/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[n]+(128/21+(32/245)*u^2+(2648/169785)*u^4+(1118492/695269575)*u^6+(14310311/87603966450)*u^8+(170868550903/10320623287474500)*u^10)*y[n+1]+(-107/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[n+2]+(-(67/1260)*h^2+(1241/198450)*h^2*u^2+(277961/366735600)*h^2*u^4+(26460409/333729396000)*h^2*u^6+(1363374533/168199615584000)*h^2*u^8+(16323847966961/19815596711951040000)*h^2*u^10)*f(n)+((188/105)*h^2+(5078/99225)*h^2*u^2+(556159/91683900)*h^2*u^4+(51834031/83432349000)*h^2*u^6+(67782373/1078202664000)*h^2*u^8+(1854079193287/291405833999280000)*h^2*u^10)*f(n+1)+((31/90)*h^2+(341/33075)*h^2*u^2+(79361/61122600)*h^2*u^4+(23456627/166864698000)*h^2*u^6+(1228061399/84099807792000)*h^2*u^8+(14797833720283/9907798355975520000)*h^2*u^10)*f(n+2)+(-(4/105)*h^2-(46/14175)*h^2*u^2-(809/1871100)*h^2*u^4-(27827/567567000)*h^2*u^6-(637171/122594472000)*h^2*u^8-(33500737/62523180720000)*h^2*u^10)*f(n+3)+((1/252)*h^2+(23/28350)*h^2*u^2+(809/7484400)*h^2*u^4+(27827/2270268000)*h^2*u^6+(637171/490377888000)*h^2*u^8+(33500737/250092722880000)*h^2*u^10)*f(n+4):

e4:=y[3] = -y[1]+2*y[2]+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(0)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(1)+((97/120)*h^2-(31/10080)*h^2*u^2-(67/302400)*h^2*u^4-(109/8870400)*h^2*u^6-(18127/31135104000)*h^2*u^8-(64931/2615348736000)*h^2*u^10-(9701/9880206336000)*h^2*u^12-(20832397/567677135241216000)*h^2*u^14-(11349439/8646159444443136000)*h^2*u^16)*f(2)+((1/10)*h^2+(31/15120)*h^2*u^2+(67/453600)*h^2*u^4+(109/13305600)*h^2*u^6+(18127/46702656000)*h^2*u^8+(64931/3923023104000)*h^2*u^10+(9701/14820309504000)*h^2*u^12+(20832397/851515702861824000)*h^2*u^14+(11349439/12969239166664704000)*h^2*u^16)*f(3)+(-(1/240)*h^2-(31/60480)*h^2*u^2-(67/1814400)*h^2*u^4-(109/53222400)*h^2*u^6-(18127/186810624000)*h^2*u^8-(64931/15692092416000)*h^2*u^10-(9701/59281238016000)*h^2*u^12-(20832397/3406062811447296000)*h^2*u^14-(11349439/51876956666658816000)*h^2*u^16)*f(4):

e5:=h*delta[0] = (-149/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[0]+(128/21+(32/245)*u^2+(2648/169785)*u^4+(1118492/695269575)*u^6+(14310311/87603966450)*u^8+(170868550903/10320623287474500)*u^10)*y[1]+(-107/42-(16/245)*u^2-(1324/169785)*u^4-(559246/695269575)*u^6-(14310311/175207932900)*u^8-(170868550903/20641246574949000)*u^10)*y[2]+(-(67/1260)*h^2+(1241/198450)*h^2*u^2+(277961/366735600)*h^2*u^4+(26460409/333729396000)*h^2*u^6+(1363374533/168199615584000)*h^2*u^8+(16323847966961/19815596711951040000)*h^2*u^10)*f(0)+((188/105)*h^2+(5078/99225)*h^2*u^2+(556159/91683900)*h^2*u^4+(51834031/83432349000)*h^2*u^6+(67782373/1078202664000)*h^2*u^8+(1854079193287/291405833999280000)*h^2*u^10)*f(1)+((31/90)*h^2+(341/33075)*h^2*u^2+(79361/61122600)*h^2*u^4+(23456627/166864698000)*h^2*u^6+(1228061399/84099807792000)*h^2*u^8+(14797833720283/9907798355975520000)*h^2*u^10)*f(2)+(-(4/105)*h^2-(46/14175)*h^2*u^2-(809/1871100)*h^2*u^4-(27827/567567000)*h^2*u^6-(637171/122594472000)*h^2*u^8-(33500737/62523180720000)*h^2*u^10)*f(3)+((1/252)*h^2+(23/28350)*h^2*u^2+(809/7484400)*h^2*u^4+(27827/2270268000)*h^2*u^6+(637171/490377888000)*h^2*u^8+(33500737/250092722880000)*h^2*u^10)*f(4):

#subroutine 3

inx:=0:
ind:=0:
iny:=1:
h:=Pi/4.0:
n:=0:
omega:=5:
u:=omega*h:
N:=solve(h*p = 500*Pi/2, p):

c:=1:
for j from 0 to 5 do
    t[j]:=inx+j*h:
end do:
#e||(1..6);
vars:=y[n+1],y[n+2],y[n+3],delta[n],y[n+4]:

printf("%6s%15s%15s%15s\n",
    "h","Num.y","Ex.y","Error y");
for k from 1 to N do

    par1:=x[0]=t[0],x[1]=t[1],x[2]=t[2],x[3]=t[3],x[4]=t[4],x[5]=t[5]:
    par2:=y[n]=iny,delta[n]=ind:
   

res:=eval(<vars>, fsolve(eval({e||(1..5)},[par1,par2]), {vars}));

    for i from 1 to 5 do
        exy:=eval(0.5*cos(5*c*h)+0.5*cos(c*h)):
        printf("%6.5f%17.9f%15.9f%13.5g\n",
        h*c,res[i],exy,abs(res[i]-exy)):
        
        c:=c+1:
    end do:
    iny:=res[5]:
    inx:=t[5]:
    for j from 0 to 5 do
        t[j]:=inx + j*h:
    end do:
end do:

A system of algebraic equation

in terms of x, y, z

how draw 3 different circles to show the range of possible values for x, y and z respectively?

it may not be a circle 

It may be 3 bounded area graph to show the range of x , y , z respectively

updated

like the graph in many examples in

algebraic and geometric ideas in the theory of discrete optimization

bound area have color

Hi, There is a problem in solving ODE using dsolve/numeric code. You people would like to help me in resolving the error, here is in attached file,

Latif_paper.mw

The following is the PDE I need to solve.

(x*y+1)*(diff(h(x, y), y, y, y))+(x+h(x, y))*(diff(h(x, y), y, y))-(diff(h(x, y), y))^2+k(x, y) = 0, (10.*(x*y+1))*(diff(k(x, y), y,y))+(10.*x+h(x,y))*(diff(k(x, y), y))-(diff(h(x, y), y))*k(x, y) = 0

This is the original boundary condition:

h(0, y) = f(y), h(x, 0) = 0, k(0, y) = g(y), k(x, 0) = 1, k(x, 25) = 0, (D[2](h))(x, 0) = 0, (D[2](h))(x, 25) = 0

After using pdsolve it come out the error:

pdsolve(eval(pde2, P = .1), pdebc4, numeric, [h(x, y), k(x, y)], spacestep = .1)

Error, (in pdsolve/numeric/par_hyp) Incorrect number of initial conditions, expected 0, got 2

If I remove one of the boundary condition when x=0, maybe h(0,y)=f(y), then the error will be this:

Error, (in pdsolve/numeric/par_hyp) Incorrect number of initial conditions, expected 0, got 1

However if I remove both when x=0, it come out this error:

Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable

May I know what is the problem of this equations?

P/S: I know its only differentiate with respect to y and is consider to be an ODE( I need more explantion on this please) and I'm still new to maple. Thanks!!

I am trying to evaluate the following double integral where hypergeom([x,1/2],[3/2],C) is gauss hypergeometric function 2f1. maple gives back it unevaluated. I doubt it may be due to slow convergence of hypergeometric function. 
 

Download DOUBLE_INT_2.mw

Hi every body,

I have a function "p(v,T)" which I evaluated its critical point. after calculating when I want to plot diagram of "p-v" for some values of "T" around critical value of "T" I expect the shape of diagram for "T" bigger and smaller than critical value of "T" be different. but it not happened. Are here anyone can help me? The function "p(v,T)" is in the file. if you want calculate critical point and check I am right or wrong. Thanks criticalpoint.mw

is it possible to change ODE to PDE?

the ODE has diff(a(t),t) and diff(b(t),t)

how to convert to diff(t, a), diff(t, b) ?