Hi,

I need your help to fix the error in this code.  many thinks
restart:
pde:=diff(u(t,x),t$2)=diff(u(t,x),x$2)-sin(u(t,x)):
f:=x->x^2:
IBC := {u(0,x)=f(x),u(t,-50)=0,D[2](u)(t, 50)=0,D[1](u)(0, x)=-diff(f(x),x)}:

pds := pdsolve(pde, IBC, numeric):

p1 := pds:-plot(t = 0);
p2 := pds:-plot(t = 1/10);
p3 := pds:-plot(t = 1/2);
p4 := pds:-plot(t = 1);
p5 := pds:-plot(t = 2);
plots[display]({p1, p2, p3, p4, p5}, title = `Sine Gordaon at t=0,0.1,0.5,1,2`);

Hi Maple-Prime-ers!

I have a system of equations, containing 18 variables and 13 equations, making this a 5 degree of freedom (DOF) system.  I would like to analytically solve each of the equations in terms of each of these DOFs.  Normally I would use solve(system, dof_variables) to accomplish this, but it doesn't return anything.  Not even [].

I can solve this system by hand.  I've included a hand-solution involving isolate() and subs() in the attached worksheet.  I'm looking to incorporate this in an optimization algorithm with varying system, so I would like an automated way of doing this.

Does anybody have any suggestions to get solve to work as intended?

3driversys_FD_BRAKE_ICE_GEN.mw

Here is the system I am talking about:

The free variables are:  {FD_T, FD_W, ICE_T, EM2_T, BRAKE_T}

I'm looking for a solution in this form:

For context, I'm designing a work sheet based around quantum tunneling. Currently I'm looking at the boundary conditions.

What I want to be able to do is to set the expression psi[1] equal to psi[2], but only for the value x = 0. Is this possible? I've tried using if statements, and I've considered converting these expressions into functions for this purpose, but I'm not having much luck. 

Thanks

Blanky

Dear all,

Please, I need help to remplace in the code attached,  addadd(beta[i]*u(x+[i]*h),i=0..N)+Error; 
by add(beta[i]*u(x+alpha[i]*h),i=0..N)+Error;  I see, that we must add a function, alpha, but how.

I think I must modify this rows: but how:

stencil := add(a[ii[i]]*subsop(r=op(r,phi)+ii[i]*stepsize,phi),i=1..N);

Question2.mw

Many thinks

Hi,

I need to solve the linear system  AX=F  without using any  Linearalgebra package. 

A is a tridiagonal matrix ( band matrix);

X is vector of size n.

F is the right hand side of my equation AX=F.

F: given, A given, Find X???

restart;

A := n-> Matrix(n,scan=band[1,1],[[seq(b[i],i=2..n)], [seq(a[i],i=1..n)],
                [seq(c[i],i=1..n-1)]] ):
X:=n->[seq(x[i],i=1..n)]:
F:=n->[seq(d[i],i=1..n)]:

Thanks

R dJ(t)/dt+J(t)/C=f(t)

where f(t) is a driving electromotive force. Use the fourier transform to analyze this equation as follows.

Find the transfer function G(alpha)  then find g(t) .

 Thanks ....

Hi,

I try to solve this equation using pdsolve but there is no results.
restart:
with(PDEtools):
with(plots):

Eq:=diff(u(t,x), t$2) =diff(u(t,x),x$2)+sin(u(t,x));

pdsolve(Eq);

Thank you for your help.

I have system of equation contain of two equations

eq1:=a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1:
eq2:=a2*x^2+b2*y^2+c2*x*y+d2*x+e2*y+f2: 

I want to find the number k so that the equation

a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1 + k*(a2*x^2+b2*y^2+c2*x*y+d2*x+e2*y+f2) = 0

can be factor, where k satisfy

a:=a1+k*a2:
b:=b1+k*b2:
c:=c1+k*c2:
d:=d1+k*d2:
e:=e1+k*e2:
f:=f1+k*f2:

I tried

A:=a*x^2+b*y^2+c*x*y+d*x+e*y+f:
collect(A,x);
B:=collect(discrim(A, x), y);
C:= discrim(B,y);

and got the expression

-16*(4*a*b*f-a*e^2-b*d^2-c^2*f+c*d*e)*a=0.

For example 

> restart:

a1:=14:

b1:=-21:

c1:=0:

d1:=-6:

e1:=45:

f1:=-14:

a2:=35:

b2:=28:

c2:=0:

d2:=41:

e2:=-122:

f2:=56:

a:=a1+k*a2:

b:=b1+k*b2:

c:=c1+k*c2:

d:=d1+k*d2:

e:=e1+k*e2:

f:=f1+k*f2:

P:=c*d*e+4*a*b*f-a*e^2-b*d^2

-f*c^2:

eq1:=a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1:

eq2:=a2*x^2+b2*y^2+c2*x*y+d2*x+e2*y+f2:

with(RealDomain):

Q:=solve(P=0,k);

factor(eq1+Q*(eq2));

solve([

eq1=0,eq2],[x,y]);

Where, Q is k which I want to find. 

My question is, if I have the system of equations

eq1:=a1*x^3+b1*y^3+c1*x^2*y+ d1*x*y^2 + e1*x+f1*y+g1:
eq2:=a2*x^3+b2*y^3+c2*x^2*y+ d2*x*y^2 + e2*x+f2*y+g2: 

How can I get a similar to the 

-16*(4*a*b*f-a*e^2-b*d^2-c^2*f+c*d*e)*a=0?

In that attached file is a multip step problem that involves graphing a right circular cylinder using transtion matrices and orthonormal basis. I have completed the hole question minus the very last part which is asking for new parametric equations for the cylinder if its center point is located at (-2, 10, 3) instead of the origin.

Any ideas on how to do this will be greatly appreciated.

question_4.mw

the sequence is non-decreasing up to some point after which it is non-increasing. Note that i can be 1 or n. A constant sequence is considered to be unimodal.

Examples of unimodal lists:

[1, 1, 1, 1, 1],
[1, 2, 2, 3, 4, 5, 5, 5],
[5, 5, 4, 4, 3, 3, 1],
[1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1],
[1, 2, 2, 3, 3, 3, 4, 4, 2, 2, 1, 1, 1]

Examples of lists that are not unimodal:

[1, 0, 1, 0],
[1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1],
[1, 1, 2, 2, 3, 4, 5, 2, 2, 6, 4, 2, 2, 1, 0]

i don't have a clue

I am trying to make a substitution:

> restart;
> f1 := conjugate(z)^2*z^2;
> f2 := applyrule(z*conjugate(z) = x, f1);

however the result is

f2 := conjugate(z)^2*z^2

Do you have any ideas how to solve the problem? Thank you.

Hi,

I have a finite difference method used to solve my problem.  My unknown function u(x,y,t) is found using the finite difference method, i would like to plot the solution for different time, and I can do this...

Only I want to make an animation in time if it's possible, and someone can help me.

Sol_animation.mw

Thnaks for helping me.

Hi, 

I love programming in Maple and I am interested in using MapleNet to display Maplets I have created. However, I am a novice in software and web technology. My questions, do I only need creating Maple worksheets, establishing interfaces and uploading the worksheets at an appropriate server in order to be able using MapleNet without any additional software? Can MapleNet display both GUI-based and command-driven-based Maplets on the web? Btw, I already read and downloaded "5 Developing Worksheets for MapleNet" but I do not fully understand its contents due to technical terms used in it.

I noticed that the following website: http://www.maplenet.net/ offers web services commercially. Does this website
have any relationship with MapleNet from Maplesoft or one of the most appropriate servers to upload and play our worksheets with MapleNet?

Thanks in advance for any helpful reply.

Loeky

email: L.Haryanto@unhas.ac.id

Hi:

how i can dimensionless a equation in maple?is there direct method for dimensionless equation in maple?for example i must dimensionless the below equation:

c1*f(x, t)+c2*(diff(phi(x, t), x))+c3*(diff(w(x, t), x, x))+c4*(diff(w(x, t), t, t)) = 0

dimensionless values are defined as:

X=x/l , T=(k/h)*t

where:

c1,c2,c3,c4 are constant cofficients.

my new equation must in terms of: X and T.

Hi, I have a homework to do that I am strugling with:

write a procedure which uses euler's method to solve a given initial value problem.
the imput should be the differential equation and the initial value.
using this programme find y(1) if dy/dx= x^2*y^3 and y(0)=1, and use maple dsolve command to check the solution.

That is what I have managed to do, but somehow it is not working correctelly, can somebody help please?

eul:=proc(f,h,x0,y0,xn)
  local no_points,x_old,x_new,y_old,y_new,i:
  no_points:=round(evalf((xn-x0)/h)):
  x_old:=x0:
  y_old:=y0:
 
  for i from 1 to no_points do
      x_new:=x_old+h:
      y_new:=y_old+evalf(h*f(x_old,y_old)):
      x_old:=x_new:
      y_old:=y_new:
  od:
  y_new:
end:


Thanks