Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I get the maple result as a product and sum off terms

 

x= (a+b*c)/d

i want to convert it to

x= a/d+b*c/d

i try to use convert(x,?)  

 

I am trying to find a general solution to the 1D-wave equation

Eq1:=diff(u(x,t),t$2)=diff(u(x,t),x$2);

pdsolve(Eq1,HINT=f(x)*g(t)); # Hinting pdsolve gives general solution using separation of variables

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)}); # without HINT and using intial conditions, I get travelling wave solution

pdsolve({Eq1,u(x,0)=f(x),D[2](u)(x,0)=g(x)},HINT=f(x)*g(t)); # Now when I try to use hint and ICs both, pdsolve return nothing.

I want to use separation of variables to find solution to the wave equation.

Any comment?

Thanks

 

It returns unevaluated.  The solution is x=-ln(3),y=0.  In fact it doesn't give a solution even if the solution is provided as the initial point.  The value of Digits doesn't seem to make a difference.

(Tested Maple 2015.2 Macintosh and Maple 2015.1 Linux)

Salut j'ai fait un programme avec maple   pour minimiser une fonction à deux variable avec la méthode de fletcher reevers car la fonction minimize ne marche pas avec les fonction plus compliqué.
SP veuillez voir mon programmme et essayer de le corriger car la boucle while ne marche pas:
test.mwtest.mw
Cordialement:

the program is not recognized kthe program is not recognized the k

I have a set of differential equations on 3 variables, B[1],B[2] and C. Its not physically meaningful for B[1]+B[2]>0.5 so i would ideally like to replace the cube that the solutions are displayed on (the axis take the limits B[1]=0...0.5,B[2]=0...0.5,C=0...100 ) with a triangular prism (the axis take the limits B[1]=0...0.5,B[2]=0...0.5,B[1]+B[2]<0.5,C=0...100 ).

Failing that i'd like the plot to display a plane showing where the meaningful values for the variables end.

here is the code I use to put the ODEplot together

Model := [diff(B[1](t), t) = k[a1]*C(t)*(R-B[1](t)-B[2](t))-k[d1]*B[1](t), diff(B[2](t), t) = k[a2]*C(t)*(R-B[1](t)-B[2](t))-k[d2]*B[2](t), diff(C(t), t) = (-(k[a1]+k[a2])*C(t)*(R-B[1](t)-B[2](t))+k[d1]*B[1](t)+k[d2]*B[2](t)+k[m]*((I)(t)-C(t)))/h];
DissMod := subs((I)(t) = 0, Model);
AssMod := subs((I)(t) = C[T], Model);

Pars1a := [k[a1] = 6*10^(-4), k[d1] = 7*10^(-3), k[a2] = 6*10^(-4), k[d2] = (7/5)*10^(-3), R = .5, k[m] = 10^(-4), C[T] = 100, h = 10^(-6)];

Pars := Pars1a; thing11 := subs(Pars, AssMod[1]), subs(Pars, AssMod[2]); thing12 := diff(C(t), t) = piecewise(t <= 100, subs(Pars, rhs(AssMod[3])), subs(Pars, rhs(DissMod[3]))); sol := dsolve({thing11, thing12, C(0) = 0, B[1](0) = 0, B[2](0) = 0}, {C(t), B[1](t), B[2](t)}, numeric, output = listprocedure, maxstep = 2, maxfun = 1000000); ParsPlot1a := odeplot(sol, [B[1](t), B[2](t), C(t)], t = 0 .. 700, color = blue, view = [0 .. .5, 0 .. .5, 0 .. 100], tickmarks = [[0 = 0, .5 = R], [0 = 0, .5 = R], [0 = 0, 25 = (1/4)*C[T], 50 = (1/2)*C[T], 100 = C[T]]]);


But I can't see a way of either making the plane or making the ODEplot axis into something other than a cube.

Could someone explain, in layman terms, what dilog and polylog are?

I don't seem to understand them from the Help and I cannot find anything on the web.

 

Thank you

Dear all

I have problem related to collection of coefficient of differtials in differential expression containing multiple dependent variables and we want to collect coefficient wrt to selected dependent variables. Please see attached Maple file for details.

 


with(PDEtools):

DepVars := [u(x, t), v(x, t), a[1](t), a[2](t), a[3](t), b[1](t), b[2](t), b[3](t), r(x, t), s[1](x, t), p[1](x, t), s[2](x, t), p[2](x, t)]

[u(x, t), v(x, t), a[1](t), a[2](t), a[3](t), b[1](t), b[2](t), b[3](t), r(x, t), s[1](x, t), p[1](x, t), s[2](x, t), p[2](x, t)]

(1)

alias(u = u(x, t), v = v(x, t), a[1] = a[1](t), a[2] = a[2](t), a[3] = a[3](t), b[1] = b[1](t), b[2] = b[2](t), b[3] = b[3](t), r = r(x, t), s[1] = s[1](x, t), p[1] = p[1](x, t), s[2] = s[2](x, t), p[2] = p[2](x, t))

u, v, a[1], a[2], a[3], b[1], b[2], b[3], r, s[1], p[1], s[2], p[2]

(2)

Suppose we differential expression like:

a[1]*(diff(u, x))*s[1]*u-2*a[1]*u*(diff(r, x))*(diff(u, x))+2*a[2]*(diff(v, x))*s[2]*v-2*a[2]*v*(diff(r, x))*(diff(v, x))-(diff(a[3], t))*r*(diff(u, x))/a[3]+diff(p[1], t)+a[3]*(diff(p[1], x, x, x))+(diff(r, t))*(diff(u, x))+(diff(s[1], t))*u-(diff(a[3], t))*s[1]*u/a[3]-s[1]*a[2]*v*(diff(v, x))-(diff(a[3], t))*a[1]*u*(diff(u, x))/a[3]-(diff(a[3], t))*a[2]*v*(diff(v, x))/a[3]-3*(diff(r, x))*p[1]+(diff(a[1], t))*u*(diff(u, x))+(diff(a[2], t))*v*(diff(v, x))+a[2]*(diff(v, x))*p[2]+a[2]*v^2*(diff(s[2], x))+a[2]*v*(diff(p[2], x))+a[1]*u*(diff(p[1], x))+a[1]*(diff(u, x))*p[1]+a[1]*u^2*(diff(s[1], x))+3*a[3]*(diff(s[1], x))*(diff(u, x, x))+3*a[3]*(diff(s[1], x, x))*(diff(u, x))+a[3]*(diff(r, x, x, x))*(diff(u, x))-(diff(a[3], t))*p[1]/a[3]-3*r*(diff(r, x))*(diff(u, x))-3*(diff(r, x))*s[1]*u+a[3]*(diff(s[1], x, x, x))*u+3*a[3]*(diff(r, x, x))*(diff(u, x, x)) = 0

3*a[3]*(diff(diff(r, x), x))*(diff(diff(u, x), x))+3*a[3]*(diff(s[1], x))*(diff(diff(u, x), x))+3*a[3]*(diff(diff(s[1], x), x))*(diff(u, x))+a[3]*(diff(diff(diff(r, x), x), x))*(diff(u, x))+a[3]*(diff(diff(diff(s[1], x), x), x))*u+diff(p[1], t)+(diff(r, t))*(diff(u, x))+(diff(s[1], t))*u-3*(diff(r, x))*p[1]+a[3]*(diff(diff(diff(p[1], x), x), x))-(diff(a[3], t))*a[1]*u*(diff(u, x))/a[3]-(diff(a[3], t))*a[2]*v*(diff(v, x))/a[3]+a[1]*(diff(u, x))*s[1]*u-2*a[1]*u*(diff(r, x))*(diff(u, x))+2*a[2]*(diff(v, x))*s[2]*v-2*a[2]*v*(diff(r, x))*(diff(v, x))-(diff(a[3], t))*r*(diff(u, x))/a[3]-(diff(a[3], t))*s[1]*u/a[3]-s[1]*a[2]*v*(diff(v, x))+(diff(a[1], t))*u*(diff(u, x))+a[1]*u*(diff(p[1], x))+a[2]*v*(diff(p[2], x))+a[2]*v^2*(diff(s[2], x))+a[2]*(diff(v, x))*p[2]+a[1]*(diff(u, x))*p[1]+a[1]*u^2*(diff(s[1], x))-(diff(a[3], t))*p[1]/a[3]-3*r*(diff(r, x))*(diff(u, x))-3*(diff(r, x))*s[1]*u+(diff(a[2], t))*v*(diff(v, x)) = 0

(3)

We can collect coefficients of differential like u[x], u[x, x], v[x], u, vin following manner:

The Procedure

   

 

 

Now how can we collect coefficents with respect to u[x], u[x, x], v[x], u, vso that differential expression (3) appear as
"(......)*u+(.......)*v+(......)*u[x]+(........)*uu[x]+(.........)vv[x]+(........)u[xx]  =0....................."????????""

``


Download Collecting_Coefficients_in_Differential_Expression.mw

Regards

We are running Maple16 in a virtual lab setup using Citrix, when exporting to PDF and saving the file to the local machine the PDF comes out as a 0kb file and the PDF is corrupt.  Has anyone else had an issue like this before?

without _Y(t) and DESol?

f := diff(u(t), t$2) + (2/t-1/t^2*p(1/t))*diff(u(t),t) + 1/t^4*q(1/t)*u(t) = 0;
dsolve(f,u(t));
u(t) = DESol({q(1/t)*_Y(t)/t^4+(2/t-p(1/t)/t^2)*(diff(_Y(t), t))+diff(_Y(t), t, t)}, {_Y(t)})

just would like to find u1 and u2 solution

In Mathematica I've a function which allows me to send a mail. I use it when I run some long time computations and I want to get an information that they are finished, etc. Is there any way to do the same thing in maple?

 

 

Hi!I am running some grid computations and I found that I could speed up my computations if my nodes could share some partial results. It seems that Grid:-Send and Grid:-Receive is almost perfect. The problem is that Grid:-Receive blocks the computations where I cannot ensure that a message will ever be send. I've tried to run Grid:-Receive on a thread in an possible infinite loop but it still blocks.

Some pieces of code below:

SignatureReciever:=proc(SigContainer::uneval,stopValue::uneval)
  while eval(stopValue) do
    SigContainer := eval(SigContainer) union {convert(Grid:-Receive(),string)};
  end do;
end proc:

SendMessage:=proc(message::string, id::integer)
  Threads[Seq](proc(i) if i <> id then Grid:-Send(i,message) end if end proc,i=0..Grid:-NumNodes()-1);
end proc:

In the main procedure run on a node I have

Threads:-Create(SignatureReciever('Signatures','stopValue'));

....

....

SendMessage(signature,id);

....

....

stopValue := false;

 

Do you have any suggestions how to solve my problem?

hi.how i can allocate infinite value for a parameter such as N ,which is attached below ( N := infinite) .i encounter with error.please see it and help

thanks..

 

restart; Digits := 55; a := 0; m := 1; n := 1; x[0] := 0; a := 0; h1 := proc (theta) options operator, arrow; cos(n*theta) end proc; h3 := proc (theta) options operator, arrow; cos(n*theta) end proc; h2 := proc (theta) options operator, arrow; sin(n*theta) end proc; N := infinite; `#mover(mi("z"),mo("&circ;"))` := z+z__c; z__c := (1/2)*h; `&lambda;__c` := E__c*`&upsilon;__c`/(-`&upsilon;__c`^2+1); `&mu;__c` := E__c/(2*(1+`&upsilon;__c`)); `&eta;__c` := E__c/(-`&upsilon;__c`^2+1); `&lambda;__m` := E__m*`&upsilon;__m`/(-`&upsilon;__m`^2+1); `&mu;__m` := E__m/(2*(1+`&upsilon;__m`)); `&eta;__m` := E__m/(-`&upsilon;__m`^2+1); E__m := 42.9*10^9; `&upsilon;__m` := .325; `&rho;__m` := 6020; E__c := 170*10^9; `&upsilon;__c` := .25; `&rho;__c` := 4640; h := 10^(-9); R := 10*h; L := 20*R; `&ell;` := 0; f := 0; `&epsilon;__r` := 0; `&epsilon;` := 8.8541878176*10^(-12)*`&epsilon;__r`; f__z := 0; `f__&theta;` := 0; f__x := 0; lambda := proc (`#mover(mi("z"),mo("&circ;"))`) options operator, arrow; (`&lambda;__m`-`&lambda;__c`)*(`#mover(mi("z"),mo("&circ;"))`/h)^N+`&lambda;__c` end proc; mu := proc (`#mover(mi("z"),mo("&circ;"))`) options operator, arrow; (`&mu;__m`-`&mu;__c`)*(`#mover(mi("z"),mo("&circ;"))`/h)^N+`&mu;__c` end proc; rho := proc (`#mover(mi("z"),mo("&circ;"))`) options operator, arrow; (`&rho;__m`-`&rho;__c`)*(`#mover(mi("z"),mo("&circ;"))`/h)^N+`&rho;__c` end proc; eta := proc (`#mover(mi("z"),mo("&circ;"))`) options operator, arrow; (`&eta;__m`-`&eta;__c`)*(`#mover(mi("z"),mo("&circ;"))`/h)^N+`&eta;__c` end proc; `D__1,0` := int(eta(`#mover(mi("z"),mo("&circ;"))`), z = -z__c .. h-z__c); `D__1,1` := int(eta(`#mover(mi("z"),mo("&circ;"))`)*z, z = -z__c .. h-z__c); `D__1,2` := int(eta(`#mover(mi("z"),mo("&circ;"))`)*z^2, z = -z__c .. h-z__c); `D__3,0` := int(lambda(`#mover(mi("z"),mo("&circ;"))`), z = -z__c .. h-z__c); `D__3,1` := int(lambda(`#mover(mi("z"),mo("&circ;"))`)*z, z = -z__c .. h-z__c); `D__3,2` := int(lambda(`#mover(mi("z"),mo("&circ;"))`)*z^2, z = -z__c .. h-z__c); `D__5,0` := int(lambda(`#mover(mi("z"),mo("&circ;"))`), z = -z__c .. h-z__c); `D__5,1` := int(lambda(`#mover(mi("z"),mo("&circ;"))`)*z, z = -z__c .. h-z__c); `D__5,2` := int(lambda(`#mover(mi("z"),mo("&circ;"))`)*z^2, z = -z__c .. h-z__c); `I__1,0` := int(rho(`#mover(mi("z"),mo("&circ;"))`), z = -z__c .. h-z__c); `I__1,1` := int(rho(`#mover(mi("z"),mo("&circ;"))`)*z, z = -z__c .. h-z__c); `I__1,2` := int(rho(`#mover(mi("z"),mo("&circ;"))`)*z^2, z = -z__c .. h-z__c); with(Student[Calculus1])

[AntiderivativePlot, AntiderivativeTutor, ApproximateInt, ApproximateIntTutor, ArcLength, ArcLengthTutor, Asymptotes, Clear, CriticalPoints, CurveAnalysisTutor, DerivativePlot, DerivativeTutor, DiffTutor, ExtremePoints, FunctionAverage, FunctionAverageTutor, FunctionChart, FunctionPlot, GetMessage, GetNumProblems, GetProblem, Hint, InflectionPoints, IntTutor, Integrand, InversePlot, InverseTutor, LimitTutor, MeanValueTheorem, MeanValueTheoremTutor, NewtonQuotient, NewtonsMethod, NewtonsMethodTutor, PointInterpolation, RiemannSum, RollesTheorem, Roots, Rule, Show, ShowIncomplete, ShowSolution, ShowSteps, Summand, SurfaceOfRevolution, SurfaceOfRevolutionTutor, Tangent, TangentSecantTutor, TangentTutor, TaylorApproximation, TaylorApproximationTutor, Understand, Undo, VolumeOfRevolution, VolumeOfRevolutionTutor, WhatProblem]

(1)

NULL

 

 

infinite.mw

Tengo una figura obtenida con ScatterPlot3D a partir de una Matriz de 3 dimensiones ( X,Y,Z ). ¿ Cómo puedo obtener la función polinómica z(x,y) que reprenta la superficie que se obtiene en el ScatterPlot3D ?

Hello,

I am trying to plot 3d scattered data as a 2d scatterplot with the third dimension being displayed as colour or a line that separates the value of the two functions (for example, the higher value and lower value at that point). I attached the file. I have two functions and several parameters that are constant. Here, I want to use P[A] on the x-axis, and P[B] on the y-axis. The z dimension is the profit functions, either Profit[1] or Profit [2]. I want to show them in colors like the highest one is red and the lower one is green, or something similar.  P[A] and P[B] are probability values and P[B] is between 0 to 0.50 with 0.01 increments, while P[A] is always less than P[B]. The file is here: example_file.mw

Example;

P[A] := 0 ..P[B]-0.01

P[B] := 0 ..0.50

Anyone please help me to code this problem.Thanks,

YC

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