Hi,

I want to solve the Falkner-Skan equation numbercally using maple. The Falkner-Skan equation is 

f′′′ + ff′′ + (1 − (f′)^2)=0 ,

with subject to the boundary conditions,

f(0) =0 ; f′(0) = 0,

f′(∞) = 1. 

could you  please help me to have loop to solve this problem from t=0..30.

And then save the data in DATfile in order to plot using Gnuplot?

Regards

the program is not recognized 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

Hi,

I am trying to use a simple sum ( f:=t,n->sum(MyFunction(k,t),k=1..n) ), but the sum function doesn't "work" :

Error, (in MTM:-sum) invalid input: ArrayTools:-AddAlongDimension expects its 2nd argument, DimToAdd, to be of type posint, but received k = 1 .. n

As far as I can understand, I have loaded the package MTM, and now, the sum has been redefined to do something else, and now I can't use a "normal" sum anymore. Or can I ?

Does someone know how to use the "normal" sum without unloading the MTM package ?

Thanks

Consider, say, the following third order derivative:

expr := diff(f(x,y),x,y$2);

Does there in Maple exist some built-in functions for extracting from such an expression 1.) the function being differentiated, and 2.) the coordinates being differentiated with respect to? Using op(expr) is of no immediate avail as it returns only a second order derivative (as the first operand), and one of the coordinates being differentiated with respect to (as the second operand).

It is, of course, possible to make ones own function for extracting these two quantities, a crude example being

splitDeriv := proc(expr,coords::expects(list) := [])
   if PDETools:-difforder(expr) > 0 then
      splitDeriv(op(1,expr),[coords[],op(2,expr)])
   else
      expr,coords
   end if
end proc:

for which

splitDeriv(expr);

But it would be much nicer to use built-in functions. And perhaps such functions do exist. If so, I am unable to locate them. Perhaps I am just being stupid, for the problem seems rather elementary.

Hello,

I have just noticed that solving a nonhomogeneous linear ode using maple dsolve gives a different solution when compared to hand calculation by method of undetermined coefficient. For instance, this equation equation is  

has the solution

Using dsolve for the same function give something completely different. Any assistance on how I can resolve this will be highly appreciated

I have the mathematica code given below. I am using Wolfram Mathematica Online.
 I am very new to Mathematica. When I put this code, I do not get any output. 
It just does not show me anything.




 \[Alpha] = 3;
 F[s_] := Exp[-A*s^(2/\[Alpha])]; integral = 
 Re[Assuming[{A > 0, t > 0, {t, A} \[Element] Reals}, 
 Integrate[F[s]*Exp[s*t] /. s -> I*y, {y, 0, Infinity}]/Pi]]

Can some help me?

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.

Download Collecting_Coefficients_in_Differential_Expression.mw

Regards

Hey,

I have an expression like this:

a:= b(t)+diff(b(t),t)+diff(b(t),t$2)+diff(b(t),t$3)+...:

I want to substitute diff(b(t),t) with b_symbol_diff. I dont know how many more differentials are in the expression.

If I use subs(diff(b(t),t)=b_symbolic_diff,a)

maple also substitutes in diff(b(t),t$2). Because b_symbol_diff is not a function of t the higher order differentials are zero.

Is there a way to tell maple not to substitute those expressions that are enclosed in diff()?

I need this because I want to calculate the Jacobian of a vector and VectorCalculus[Jacobian]() does not accept functions.

Thanks in advance!

I am having difficulty helping someone series expand an eigenvector solution.  I can expand the eigenvalues easily but get a numeric exception divide by zero when I attempt to expand a component of an eigenvector.  Mathematica seems to have no problem solving this problem.  Any help would be appreciated.

Download CourseraOpticsEigenvalues.mwCourseraOpticsEigenvalues.mw

Hello

How can i get whether a radio box is checked or not through another button action window. I have attached a picture of my question. Could you please help me to solve it.

 Thank you

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

how to transform this differential equation with a substitution?

f := diff(u(x),x$2) + p(x)*diff(u(x),x)+q(x)*u(x)=0;
transformed := subs(x=1/t, f);

f := diff(u(x),t$2)*diff(t,x$2) + p(x)*diff(u(x),t)*diff(t,x)+q(x)*u(x)=0;

diff(1/t,t);
diff(1/t,t$2);

x = 1/t
dx/dt = -1/t^2
d2x/dt2 = 2/t^3

d2u/dt2*dt2/dx2
du/dt*dt/dx
diff(u(t),t$2)*1/(2/t^3) + p(t)*diff(u(t),t)*1/(-1/t^2)+q(t)*u(t)

restart;
f := u2*1/(2/t^3) + p(t)*u1*1/(-1/t^2)+q(t)*u;
f2 := collect(f/t^3*2, {u2, u1, u});
subs(u2 = diff(u(t),t$2), subs(u1 = diff(u(t), t), subs(u=u(t), f2)));

but not equal to below which is in book, is this equation wrong in book?

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;