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dharr

Dr. David Harrington

8837 Reputation

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21 years, 121 days
University of Victoria
Professor or university staff
Victoria, British Columbia, Canada

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Contact Dr. David Harrington
I am a retired professor of chemistry at the University of Victoria, BC, Canada. My research areas are electrochemistry and surface science. I have been a user of Maple since about 1990.

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These are replies submitted by dharr

Can't assign to F...

dharr 8837
February 12 2017
0 0

@mehdibaghaee If you use F[3,1] etc in your integrand, then you can't use the variable F to assign the result of the dchange - just change it to FF or something else

2-D vs 1-D...

dharr 8837
February 12 2017
0 0

@nk2016  You will get the right result if you paste into 1-D Maple (try control-M on the line before you paste), but if you paste into 2-D, the != characters change into "not equal to" and you get a quite different result.

add to dchange...

dharr 8837
February 12 2017
0 0

@mehdibaghaee 


 

``

> 

PDEtools:-dchange({x = (1/2)*a*(xi+1), y = (1/2)*b*(eta+1)}, T, [xi, eta], params = [a, b], known = u0)

(1/2)*(int((1/2)*(int((1/2)*I__0*(D[3](u0))((1/2)*a*(xi+1), (1/2)*b*(eta+1), t)^2*b, eta = -1 .. 1))*a, xi = -1 .. 1))

 (3)

NULL

NULL

The idea is that if you are solving, say, dy(x)/dx = -k*y(x) with y(0)=1 (y(x) is "unknown") the solution is y(x)=exp(-k*x), and if you change variables x=2*X, then the solution is y(X)=exp(-2*k*X) in which y(X) is a different function than y(x). But if you have a known function like sin(x) then you want sin(x) to change to sin(2*X)
 

Download inttt3.mw

known function...

dharr 8837
February 12 2017
0 0

@mehdibaghaee  add known=u0 to get this.

Try dchange...

dharr 8837
February 11 2017
0 1

@mehdibaghaee Looks like a bug

Using dchange gives the expected double integral
 

NULL

> 

PDEtools:-dchange({x = (1/2)*a*(xi+1), y = (1/2)*b*(eta+1)}, T, [xi, eta], params = [a, b])

(1/2)*(int((1/2)*(int((1/2)*I__0*(diff(u0(xi, eta, t), t))^2*b, eta = -1 .. 1))*a, xi = -1 .. 1))

 (3)

``

``


 

Download inttt2.mw

and the loop is not right...

dharr 8837
December 26 2016
0 0

aside from the main issue raised by @rlopez your loop should be "from 0 to 99" not "by 0 to 99"

fsolve works for me...

dharr 8837
December 05 2016
0 0

@umar khan  

fsolve(y, x = 0 .. 2e6);

works for me.

A special case?...

dharr 8837
November 30 2016
0 1

@leslieglasser Still not clear what the possible inputs are. If it is a monic polynomial and the other coefficents are the variables (as in your example), then the following works:


 

> 

restart;with(LinearAlgebra):
> 

n:=4;
p:=w^n+add(a[i]*w^i,i=0..n-1);

4

  

w^4+w^3*a[3]+w^2*a[2]+w*a[1]+a[0]

 (1)
> 

M1:=<seq(a[n-i],i=1..n)>:M2:=<seq(w^(n-i),i=0..n)>^(%T):
> 

M:=<<M1|DiagonalMatrix([-1$n])>,M2>;
Determinant(M);

M := Matrix(5, 5, {(1, 1) = a[3], (1, 2) = -1, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = a[2], (2, 2) = 0, (2, 3) = -1, (2, 4) = 0, (2, 5) = 0, (3, 1) = a[1], (3, 2) = 0, (3, 3) = 0, (3, 4) = -1, (3, 5) = 0, (4, 1) = a[0], (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = -1, (5, 1) = w^4, (5, 2) = w^3, (5, 3) = w^2, (5, 4) = w, (5, 5) = 1})

  

w^4+w^3*a[3]+w^2*a[2]+w*a[1]+a[0]

 (2)
> 

 

I don't have any suggestions for more complicated cases.
 

Download Companion3.mw

Need more info...

dharr 8837
November 30 2016
0 0

@leslieglasser  Well you can make a 3x3 one by bordering the 2x2 one with zeroes except for one in the 1,1 entry. But I'm guessing that isn't what you want. Can you be more specifc about your exact requirements? - I don't know what separated variables mean or nomograph in this context.

closer?...

dharr 8837
November 15 2016

int(Heaviside(1-x^2-y^2), [x=0..1,y=0..1]); #should be Pi/4

gives -Pi/4

(I thought using even symmetry might help, but it went negative.)

Set x...

dharr 8837
November 02 2016
0 0

@dharr If you set x=Pi/2 rather than solving for it, then you get the a, b, c values that you want.

Not correct solution...

dharr 8837
October 27 2016
0 0

ab should be a*b, but if I've interpreted your equation correctly, then odetest suggests that your solution is not correct.

diff(psi(x), x, x)-((b^2-a*(2*p+3))*x^2+2*a*b*x^4+a^2*x^6-energy)*psi(x) = 0;
schro := eval(%,energy=(2*p+1)*b);
odetest(psi(x)=(x^p)*exp((-a*(x^4))/4)-(b*(x^2)/2),schro);

does not return zero, meaning it is not a solution. Using dsolve gives something with Heun functions, but you probably need to check you have the right equation first.

complicated...

dharr 8837
July 28 2016
0 0

@sunit I'm not entirely sure what you mean. You could certainly write a procedure that tested whether there were minus signs to its argument and adjusted things before passing to sin. But covering all the unexpected cases (the above one was certainly unexpected for me; I just mistakenly typed Phi instead of phi) is probably going to take more effort than it is worth. As I noted, Maple isn't human, and often outputs things in forms that are unexpected (but mathematically correct)

Maple has a mind of its own...

dharr 8837
July 28 2016
0 0

> 

restart;
> 

q1:=sin(omega*(T0-T)+Phi);

sin(omega*(T0-T)+Phi)

 (1)
> 

map(expand,q1);

sin(-T*omega+T0*omega+Phi)

 (2)
> 

q2:=sin(omega*(T0-T)+phi);

-sin(-omega*(T0-T)-phi)

 (3)

Notice the Maple has changed rearranged to have a minus before the sin.

> 

map(expand,q2);

-sin(omega*T)*cos(omega*T0)*cos(phi)+sin(omega*T)*sin(omega*T0)*sin(phi)+cos(omega*T)*sin(omega*T0)*cos(phi)+cos(omega*T)*cos(omega*T0)*sin(phi)

 (4)

map applies expand to each operand. For q1, the only operand is the argument to sin, but Maple considers q2 as a product of two operands, the -1 and the sin, so it expands both

> 

whattype(q1);op(q1);

function

  

omega*(T0-T)+Phi

 (5)
> 

whattype(q2);op(q2);

`*`

  

-1, sin(-omega*(T0-T)-phi)

 (6)

To get what you want requires you to operate the expand on the (first) operand of the second operand, which can be done as follows

> 

applyop(expand,[2,1],q2);

-sin(T*omega-T0*omega-phi)

 (7)

But this is a rather complicated solution, which requires attention in individual cases. Of course you could just stick with Phi. In general, getting Maple to rearrange things into the exact form you want is difficult. Depending on your ultimate objective, it may not be worth it. But perhaps others have a simpler solution.

> 

 


Download expand2.mw

@sunit 

 

OK...

dharr 8837
July 21 2016

I misread the correct answer at line (13) followed by the comment "The results are worse than single iteration using jacobian" to mean that you didn't think the default solver was working. I see you have now clarified that with an edit.

As for correctly coding lsode I don't have much comment; I have tried to move away low level coding.

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