How do I find all the solutions to a trigonometric...

Hello,

I have just started using Maple, and it seems very powerful. I am trying to solve trigonometric equations and get all the solutions in a range, but when I use fsolve I only get one solution.

Is this by design of the function or is there another way to do this?

Tom

how to obtained the graph in exp form...

i need to find the graph of exp(v(r)) from 0 to 2e6.

i obtained the graph of v(r) by taking log but how to obtained in exp form

error in f(solve)...

I can't make maple solve this equation, any help please

a problem with fsolve...

hi

thanks

 > restart:
 > F(eta):=sum(a[i]*eta^i,i=0..5):
 > theta(eta):=sum(b[i]*eta^i,i=0..5):K(eta):=sum(c[i]*eta^i,i=0..5):Omega(eta):=sum(d[i]*eta^i,i=0..5):
 >
 > U1:=diff(theta(eta), eta, eta)-3*Omega(eta)*(F(eta)*(diff(theta(eta), eta))-theta(eta)*(diff(F(eta), eta)))/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(theta(eta), eta)) = 0:U2:= diff(F(eta), eta, eta, eta)+Omega(eta)*(3*F(eta)*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2)/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(F(eta), eta, eta))+Omega(eta)/K(eta) = 0:U3:= diff(K(eta), eta, eta)+Omega(eta)*(1.5*F(eta)*(diff(K(eta), eta))-K(eta)*(diff(F(eta), eta)))/K(eta)+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(K(eta), eta))+(diff(F(eta), eta, eta))^2-Omega(eta)^2 = 0:U4:= diff(Omega(eta), eta, eta)+Omega(eta)*(3*F(eta)*(diff(Omega(eta), eta))+Omega(eta)*(diff(F(eta), eta)))/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(Omega(eta), eta))+Omega(eta)*(diff(F(eta), eta, eta))^2/K(eta)-Omega(eta)^3/K(eta) = 0:
 > F(eta):=unapply(F(eta),eta):
 > theta(eta):=unapply(theta(eta),eta):K(eta):=unapply(K(eta),eta):Omega(eta):=unapply(Omega(eta),eta):
 > U1:=unapply(U1,eta):U2:=unapply(U2,eta):U3:=unapply(U3,eta):U4:=unapply(U4,eta):
 >
 > s1:=F(eta)(0) = 0:
 > s2:=K(eta)(0) = 0:s3:=Omega(eta)(0) = 0:s4:=theta(eta)(0) = 1:s5:=theta(eta)(1) = 0:s6:=(D(F(eta)))(0) = 0:s7:=(D(K(eta)))(1) = 0:s8:=(D(Omega(eta)))(1) = 0:s9:=((D@@2)(F(eta)))(1) = 0
 (1)
 > s10:=U1(0):s11:=U2(0):s12:=U3(0):s13:=U4(0):        s14:=U1(1):s15:=U2(1):s16:=U3(1):s17:=U4(1):    s18:=D(U1)(0):s19:=D(U2)(0):s20:=D(U3)(0):s21:=D(U4)(0):     s22:=D(U1)(1):s23:=D(U2)(1):s24:=D(U3)(1):
 >
 >
 > Q:=fsolve([s1,s2,s3,s4,s5,s6,s7,s8,s9,s10,s11,s12,s13,s14,s15,s16,s17,s18,s19,s20,s21,s22,s23,s24],{a[0],a[1],a[2],a[3],a[4],a[5],b[0],b[1],b[2],b[3],b[4],b[5],c[0],c[1],c[2],c[3],c[4],c[5],d[0],d[1],d[2],d[3],d[4],d[5]}):
 > F(eta):=eval(sum(a[i]*eta^i,i=0..5),Q):
 > theta(eta):=eval(sum(b[i]*eta^i,i=0..5),Q):K(eta):=eval(sum(c[i]*eta^i,i=0..5),Q):Omega(eta):=eval(sum(d[i]*eta^i,i=0..5),Q):
 > plot(g(x),x=0..1,axes=boxed,color=green,thickness=2,labels=[x,g]):
 > plot(f(x),x=0..1,axes=boxed,color=blue,thickness=2,labels=[x,f]):
 >

fsolve 3 exponential equations with 3 unknown term...

 (1)

 (2)

 (3)

 (4)

 (5)

it would be great if you could explain me why maple cant numerically solve this set of 3 ecuatios for h1, h2, k being my unknows terms, it works with an exponential function. there is a way to solve it?

thanks..

How can I make fsolve return a solution for a syst...

So I am trying to find the structure of a material from x-ray diffraction data. To accomplish this I have to solve a system of nonlinear equations. Since there is some unaccuracy in the measurements I wanted to use a numerical tool, so I am trying to solve using fsolve. To check that I am doing this correctly I am trying to solve a set of similar equations where I know the solution. My code is shown below.

eqs := {(2^2/a^2+2^2/c^2-2*(2*2)*cos(x)/(a*c))/sin(x)^2 = 1/2.2393^2, (2^2/a^2+4^2/c^2+4*(2*2)*cos(x)/(a*c))/sin(x)^2 = 1/1.5968^2, (1^2/a^2+sin(x)^2/b^2+2^2/c^2+(2*2)*cos(x)/(a*c))/sin(x)^2 = 1/2.7896^2, 1/sin(x)^2*(2^2*sin(x)^2/b^2) = 1/2.8650^2}

fsolve(eqs)

For this system I know that a = 5.44 b = 5.73 c = 7.89 x=pi/2, but fsolve only returns the input.

Am I doing something wrong or should I use a different function? I am quite new to Maple, so have some patience with me.

Error, (in fprintf) number expected for floating p...

Very new to using Maple or coding in general. Ran into a problem that I couldn't figure it out.

Any help would be greatly appreciated.

Problem with integrating a solution from fsolve...

I have a problem integrating a solution from fsolve.   I read in another post on this forum that the solution was to use unapply.   This works if I then set up the integration as suggested (i.e., without giving the argument to the function), but not if you do it in a way that seems logical to me (i.e.,the first version of the int command marked ‘fails’ below.   if you can plot a function why can’t you integrate it ?).

Anyway the real problem I have is if I want to use the solution found using fsolve as the argument of another function (h below) and then integrate that.  I assume the final line fails because of the same reason the initial attempt to integrate g(x) fails. However, I can’t figure out what the equivalent notation would be if I wanted to omit the ‘x’ variable.   I tried using unapply again, and also putting in quotes, but nothing works.

> restart;

> g:=unapply('fsolve(a*y^2-sin(y),y=2)',a);

> plot('g(x)',x=1..2);

> evalf(Int('g(x)',x=1..2));#this fails

> evalf(Int(g,1..2));#this works fine

> h:=x->x*sin(x);

> h(g(1.0));

> h(g(2.0));

> evalf(Int(h(g(x)),x=1..2));# this fails

How to solve transcendental equation exactly?...

I mean the root of the equation

GAMMA(n-1/n)*GAMMA(1/n)/(n*GAMMA(n)) = 1

belonging to RealRange(Open(1),4). It should be noticed there are solutions outside this interval. Here is my try.

 (1)

 (2)

Also

 (3)

There is a substitute

 (4)

 (5)

There is a shade of hope that GAMMA(n-1/n)*GAMMA(1/n)/(n*GAMMA(n))  can be simplified.

PS. An SCR was submitted by me.

Why fsolve don't solve this system ?...

Hello all,

I try to solve this system using maple 18 by "fsolve", but I don't get the solution, I don't Know what is the problem or What this mean.

Do you have any idea?

Best Regards L.Sn=10_R=23.5.mw

fsolve doesnt work for many unknowns ...

Hey there,

I am using the fsolve command in order to solve numerically a system of equations with N equations and N unknowns. According to my discretization the number of equations changes. If I have a small number of equations it all works out perfectly. But if I increase the number of equations I just get something like that:

Sorry, for the long post, but for a small number of unknowns Ai it works. It seems that maple doesnt try to compute? Has anyone encountered the same problems?

Any help is appreciated.

Jens

Find the solution by using fsolve?...

Table_1_for_example_1.mw

I am try to find root by using fsolve. But I am not get solution.

I have been attached the program above.

Thank You.

Best Regards.

Velmurugan G

How does Maple determine the interval for function...

In functions such as fsolve, there is an optional parameter that allows one to specify the interval to perform the function on. Additionally, sometimes, if a solution is left out, one can specify an interval to search on to obtain the missing solution.

How does Maple determine the interval to search on if this is not specified?

(Additional Question - you don't have to answer this)

Ultimately, I am asking this question because I have a function for Newton's method; however, it requires an interval to run. I have read that fsolve uses Newton's method, so I am curious how to automatically select such an interval. Does anyone know how to implement such a thing?