Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

Hey there,

I've been struggling for a few days to integrate a function using rkf45.

For some context, I wish to numerically intergrate a function K * s_R (K,a,w) dK using runge kutta over a 2D grid of (a,w) values. Essentialy, performing the same sort of K-integral many different times for slightly different combinations of a and w. For one such (a,w) combination, the function looks something like this:

and rkf45 works just fine, and returns a numeric result. On the other hand, for a different combination of (a,w), the function looks like this:

and an attempt to perform rkf45 returns the following error: "cannot evaluate the solution past the initial point, problem may be complex, initially singular or improperly set up."

Here is a simplified version of my maple document for reference MaplePrimePleaseHelp.mw.

I'm happy to clarify anything that may be confusing and any thoughts or suggestions would be greatly appreciated.

Thank you!

I have a physics question I need to program it by Maple , Can you help me to solve ? Its Problem 9.34 from Griffiths

Hey there,

I'm trying to numerically intergrate a function s(K,i,j) dK using runge kutta over a 2D grid of i,j values. Essentialy, performing the same sort of integral many different times for slightly different combinations of i and j. The function is more or less gaussian, and so the bulk of the result will come from the values of K around the peak of said gaussian. For some combinations of i and j, the function seems to have a singularity on the right edge of the gaussian peak, which causes my script to spit out an error, telling me the calculation cannot be performed further to the right past the singularity. Now, like i said before, the singularity is on the very edge of the gaussian and therefore I am perfectly happy to stop the integration before the singularity, because anything past it wont contribute very much to the result.

How can I use dsolve events to halt my integration just before hitting the singularity?

RK := (i, j) -> dsolve({diff(n(K), K) = K*s(K, a[i], b[j]), n(0) = 0}, numeric, method = rkf45)

 

In the uploaded worksheet a block slides up the Hill from an initial position at an initial horizontal velocity. The block's motion is subject to sliding friction.

How can the equations of the block's motion be obtained to include the effects of gravity and friction?

It may simplify the answer to end the block's upward motion when gravity and friction bring it to an instantaneous halt.

Block_sliding.mw

Hi

How can i solve this system of equations:
{c*(N-k)*(1-exp(-p)) = p, -d*((k-N)*exp(-p)-k) = N, 0 < N, 0 < p, 1 < c, 1 < d, 1 < k}

N and P are variables and the others are constant numbers.

I used "solve" function but the results are:
piecewise(And(1 < c, 1 < d, 1 < k, 0 < -RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z)*d/((d-1)*c), 0 < -RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z)), [{N = d*k*(exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))-1)/(d*exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))-1), p = c*k*(d*exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))-d-exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))+1)/(d*exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))-1)}], [])

piecewise(And(1 < c, 1 < d, 1 < k, 0 < -RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z)*d/((d-1)*c), 0 < -RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z)), [{N = d*k*(exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))-1)/(d*exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))-1), p = c*k*(d*exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))-d-exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))+1)/(d*exp(RootOf(exp(_Z)*c*d*k+exp(_Z)*_Z*d-exp(_Z)*c*k-c*d*k+c*k-_Z))-1)}], [])

 

 

 

During running my ws I faced with memory error as below, where as my system have enough memory (120GB)

Warning, Run: unable to set assignto result due to error:  Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc

Maple's help suggests :Software limits are imposed by the -T command-line argument, the datalimit argument to kernelopts and system imposed user limits (for example shell limits).
  But I could not understand how to increase software limit.

 

how to fix that?

I unprotect the GAMMA, but still receives error:

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.


 

NULL

restart

II := 2

2

(1)

JJ := 2

2

(2)

N := 2:

unprotect(GAMMA):

q := max(II+1, JJ+1):

M := 5:

seq(seq(seq(assign(GAMMA[i, j, r], a*`#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[i, j, r]), i = 0 .. q), j = 0 .. q), r = 1 .. N):

a := .2:

RrProc := proc (i, m) local K, j, Q; if i <= m then 0 else K := 1; Q := Matrix(i, 1); for j by 2 to i do Q(j) := 2*i-K; K := 4+K end do; Q := FlipDimension(Q, 1); Q(m+1) end if end proc:
``

`#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))` := Array(0 .. II, 0 .. JJ, 1 .. 6, 1 .. M):

f1 := RandomArray(II+1, JJ+1):

for m to M do `&Gamma;m`[1, m] := f1; `&Gamma;m`[2, m] := f2; `&Gamma;m`[3, m] := f3; `&Gamma;m`[4, m] := f4; `&Gamma;m`[5, m] := f5; `&Gamma;m`[6, m] := f6 end do:

unprotect(`#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`):

for m to M do `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 1, m] := ArrayTools:-Alias(`&Gamma;m`[1, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 2, m] := ArrayTools:-Alias(`&Gamma;m`[2, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 3, m] := ArrayTools:-Alias(`&Gamma;m`[3, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 4, m] := ArrayTools:-Alias(`&Gamma;m`[4, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 5, m] := ArrayTools:-Alias(`&Gamma;m`[5, m], [0 .. II, 0 .. JJ]); `#mover(mi("&Gamma;",fontstyle = "normal"),mo("&uminus0;"))`[0 .. II, 0 .. JJ, 6, m] := ArrayTools:-Alias(`&Gamma;m`[6, m], [0 .. II, 0 .. JJ]) end do:

UP := proc (s, GAMMA, N, M, a, b, II, JJ) local k; i, j, r, p, m, q, n, l; if s = 1 then add(add(add(add(add(add((2/3)*Rr[i, m]*Rr[k, m]*b*add(GAMMA[i, j, q, p]*GAMMA[k, j, q, r]*tau[p](t)*tau[r](t), q = 1 .. N)/((2*m+1)*(2*j+1)*a), i = 0 .. II), k = 0 .. II), m = 0 .. II), j = 0 .. JJ), p = 1 .. M), r = 1 .. M) elif s = 2 then add(add(add(add(add(add((1/2)*Rr[i, m]*Rr[k, m]*b*add(GAMMA[i, j, q, p]*GAMMA[k, j, q, r]*tau[p](t)*tau[r](t), q = 1 .. N)/((2*m+1)*(2*j+1)*a), i = 0 .. II), k = 0 .. II), m = 0 .. II), j = 0 .. JJ), p = 1 .. M), r = 1 .. M) end if end proc:

Grid:-Seq(UP(s, GAMMA, N, M, a, b, II, JJ), s = 1 .. 2)

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.

 

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.

 

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.

 

Error, attempting to assign to `GAMMA` which is protected.  Try declaring `local GAMMA`; see ?protect for details.

 

UP(1, GAMMA, N, M, a, b, II, JJ), UP(2, GAMMA, N, M, a, b, II, JJ)

(3)

NULL


 

Download soal.mw

 

What is the problem?

 

Dear all,

Greeting!

I am a new user of Maple. I want to perform a simple (to me, it is very difficult) integration  defined as follows 

range from 0 to omega (frequency). alpha^2F (omega) is constant function with set of values (already calculated) for the corresponding frequency. I have calculated the frequencies ranging from 54 to 900 cm-1. Suppose I have alpha^2F(omega)=0, 0.5,0.6,0.7......0.1 for omega=58, 80, 110, 190,.....800, how can I perform this integration  in Maple? Please help me how can I cope with this problem.

Thanks a lot.

Best Regards,

 

I would like to animate the motion of a bicycle racer on a classic velodrome track i.e. one with varied vertical and horizontal curvatures along its length.

Is there a source which explains the math expressions which model the shape of such a track?

Hi

I have the values of of a function A(x,y,z) in 3d cartesian coordinates as [x[1],y[1],z[1],A(x[1],y[1],z[1])], [x[2],y[2],z[2],A(x[2],y[2],z[2])], [x[i],y[i],z[i],A(x[i],y[i],z[i])],etc...where i vary from 1 to 300 (or higher).

How to plot A(x[i],y[i],z[i]) in 3d.

Thanks

How can I plot functions Vc=(0.5+t)^n

with t=z/h, 

Hi there,

I have difficulties in solving the first partial derivatives dw/db and dw/dvarphi of this equation with its constraint:

w := exp(exp(x*b)*(r-1)/(1+varphi*exp(x*b))) where ln(r) = varphi*(exp(x*b))(r-1)/(1+varphi*exp(x*b))-1

Please help.

Regards,

Sarni Berliana

Hello, 

I am fairly new to using the Maple software, so I apologize if my question is completely idiotic. Apologies, also, because I could not manage to enter my code as code. When I pressed the button it made the whole text as a code. 

I run the following code to seek -if there are any- analytic solutions for the following differential equation.

odeplus := (r^2+L^2)^(5/2)*(diff(f(r), `$`(r, 2)))+((15/4)*r*(r^2+L^2)^(1/2)+3*(r^2+L^2)^(5/2)/r)*(diff(f(r), r))+M^2*f(r)/(r^2+L^2)^(5/2)-((5/2)*((r^2+L^2)^(1/2))(l-1)+(55/64)*r^2/(r^2+L^2)^(3/2)+(r^2+L^2)^(5/2)*(l^2+3*l+3/2)/r^2)*f(r)+(((r^2+L^2)^(1/2))(5+(5/2)*l)+(5/8)*r^2/(r^2+L^2)^(3/2)-(r^2+L^2)^(5/2)*(3/2+l)/r^2)*f(r) = 0

and then I do 

dsolve(odeplus, f(r))

The solutions that Maple returns is given in terms of DESol. Could anyone try and break it down for me? What is this telling me and if I can indeed from the output obtain analytic solutions? Is this some sort of operator acting on something? 

Thank you in advance. 

`~`[int](convert(convert(series(x^x, x), polynom), list), x = 0 .. 1)

Can this sequence (produced above in list form) be displayed as 1, -1/2^2, 1/3^3, -1/4^4, 1/5^5 -1/6^6 etc.

That is with the powers unevaluated.

Please describe the step-by-step application of the rules of differentiation which produce this derivative:

diff(a(x)^b(x), x) =        

a(x)^b(x)*((diff(b(x), x))*ln(a(x))+b(x)*(diff(a(x), x))/a(x));

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