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Hello there

I'm quite an amature so please don't judge.  I'm trying to use fsolve to solve a system of non-linear equations but Maple is just "spitting" on me the equations with no intention to solve them:

> delta5 := P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+zeq^2)*(sqrt(x^2+zeq^2)*x))+x*zeq/sqrt(x^2+zeq^2)^3)/(2*Pi*E5);
print(`output redirected...`); # input placeholder
> shrinkage := P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+Zb^2)*(sqrt(x^2+Zb^2)*x))+x*Zb/sqrt(x^2+Zb^2)^3)/(2*Pi*E5)-P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+Za^2)*(sqrt(x^2+Za^2)*x))+x*Za/sqrt(x^2+Za^2)^3)/(2*Pi*E5);
> eq10 := subs(x = 1800, delta5)+subs(x = 1800, Zb = z2, Za = z1, shrinkage)+subs(x = 1800, Zb = z3, Za = z2, shrinkage)+subs(x = 1800, Zb = z4, Za = z3, shrinkage)+subs(x = 1800, Zb = z5, Za = z4, shrinkage) = 36.7*10^(-3);
print(`output redirected...`); # input placeholder
> eq9 := subs(x = 1500, delta5)+subs(x = 1500, Zb = z2, Za = z1, shrinkage)+subs(x = 1500, Zb = z3, Za = z2, shrinkage)+subs(x = 1500, Zb = z4, Za = z3, shrinkage)+subs(x = 1500, Zb = z5, Za = z4, shrinkage) = 47.2*10^(-3);
print(`output redirected...`); # input placeholder
> eq8 := subs(x = 1200, delta5)+subs(x = 1200, Zb = z2, Za = z1, shrinkage)+subs(x = 1200, Zb = z3, Za = z2, shrinkage)+subs(x = 1200, Zb = z4, Za = z3, shrinkage)+subs(x = 1200, Zb = z5, Za = z4, shrinkage) = 63.8*10^(-3);
> eq7 := subs(x = 900, delta5)+subs(x = 900, Zb = z2, Za = z1, shrinkage)+subs(x = 900, Zb = z3, Za = z2, shrinkage)+subs(x = 900, Zb = z4, Za = z3, shrinkage)+subs(x = 900, Zb = z5, Za = z4, shrinkage) = 91.1*10^(-3);
print(`output redirected...`); # input placeholder
> eq6 := subs(x = 600, delta5)+subs(x = 600, Zb = z2, Za = z1, shrinkage)+subs(x = 600, Zb = z3, Za = z2, shrinkage)+subs(x = 600, Zb = z4, Za = z3, shrinkage)+subs(x = 600, Zb = z5, Za = z4, shrinkage) = 137.9*10^(-3);
> eq5 := subs(x = 450, delta5)+subs(x = 450, Zb = z2, Za = z1, shrinkage)+subs(x = 450, Zb = z3, Za = z2, shrinkage)+subs(x = 450, Zb = z4, Za = z3, shrinkage)+subs(x = 450, Zb = z5, Za = z4, shrinkage) = 175.2*10^(-3);
> eq4 := subs(x = 300, delta5)+subs(x = 300, Zb = z2, Za = z1, shrinkage)+subs(x = 300, Zb = z3, Za = z2, shrinkage)+subs(x = 300, Zb = z4, Za = z3, shrinkage)+subs(x = 300, Zb = z5, Za = z4, shrinkage) = 230.9*10^(-3);
print(`output redirected...`); # input placeholder
> sys := {eq10, eq5, eq6, eq7, eq8, eq9};
print(`output redirected...`); # input placeholder
> fsolve(sys, {E1 = 1000 .. 2000, E2 = 0 .. 2000, E3 = 0 .. 2000, E4 = 0 .. 2000, E5 = 0 .. 2000, h4 = 100 .. 400});

and this is what Maple gives after the fsolve

 

fsolve({(3937.500000*(.2/(202500+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(450*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(202500+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.3888888889e-2/E5+(3937.500000*(.2/(202500+(650+h4)^2)+(450*(650+h4))/(202500+(650+h4)^2)^(3/2)))/E5 = .1752000000, (3937.500000*(.2/(360000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(600*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(360000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.2187500000e-2/E5+(3937.500000*(.2/(360000+(650+h4)^2)+(600*(650+h4))/(360000+(650+h4)^2)^(3/2)))/E5 = .1379000000, (3937.500000*(.2/(810000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(900*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(810000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.9722222220e-3/E5+(3937.500000*(.2/(810000+(650+h4)^2)+(900*(650+h4))/(810000+(650+h4)^2)^(3/2)))/E5 = 0.9110000000e-1, (3937.500000*(.2/(1440000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1200*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(1440000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.5468750000e-3/E5+(3937.500000*(.2/(1440000+(650+h4)^2)+(1200*(650+h4))/(1440000+(650+h4)^2)^(3/2)))/E5 = 0.6380000000e-1, (3937.500000*(.2/(2250000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1500*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(2250000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.3500000000e-3/E5+(3937.500000*(.2/(2250000+(650+h4)^2)+(1500*(650+h4))/(2250000+(650+h4)^2)^(3/2)))/E5 = 0.4720000000e-1, (3937.500000*(.2/(3240000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1800*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(3240000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.2430555555e-3/E5+(3937.500000*(.2/(3240000+(650+h4)^2)+(1800*(650+h4))/(3240000+(650+h4)^2)^(3/2)))/E5 = 0.3670000000e-1}, {E1, E2, E3, E4, E5, h4}, {E1 = 1000 .. 2000, E2 = 0 .. 2000, E3 = 0 .. 2000, E4 = 0 .. 2000, E5 = 0 .. 2000, h4 = 100 .. 400})

I have an equation,

     y = 2x2+7,

Plotting y against x will give a quadratic graph, but plotting y against x2 should give a straight line. The problem is I cannot do

  plot([y], x2 = -5 .. 5);

It gives me an error

    Error, (in plot) unexpected option: x^2 = -5 .. 5

I have searched online but no links. Can anyone help with this.

 

Thanks

Fairoz

 

 

Hi, I'm new to Maple and was trying to use it to solve 3 equations with 3 unknowns, in terms of another 2 parameters. This is what I put in, and the error that came up:

solve({(1-x)/(1+b) = b*y, (1-y)(1-a)/(-a*b+1) = b*z, (1-z)(1-b)/(-a*b+1) = a*x}, {x, y, z}); 

Error, (in SolveTools:-LinearSolvers:-Algebraic) unable to compute coeff

I want to solve the equations to get x,y,z in terms of a,b but I don't understand the error coming up - have I done something wrong or is it because not all the variables appear in all of the equations? As there are 3 equations and 3 unknowns there is a solution, but I want to check the answer I found on paper with something (the algebra got a bit messy!)

Any help greatly appreciated! :)

Is it possible to define and use an abstract linear operator L which is a function of y(x) and z(x)? 

For example, Maple should be able to recognise that L(y(x),z(x)) = L(z(x),y(x)) and simplify expressions such as 

L(c*y(x),d*z(x)) = c*d*L(y(x),z(x)) where c and d are constants or numbers.

It should also be able to expand things like L(c*y1(x)+d*y2(x),e*z1(x)+f*z2(x)).

Thanks.

I've got a function f(x_n) = (x_n-1)^3

and need to show that for the iterative method

x_(n+1)= x_n - f(x_n)/(sqrt(f'(x_n)^2-f(x_n)*f''(x_n), at a simple root we have cubic convergence while at a multiple root, it converges linearly.

I understand that the approach is to write either a recursive function or a sequence, but i'm confused about the structure since both x and n are being incremented

 

Hello guys

I have a coupled linear differentional equation which are in the 4th order. they are shown in the below:

P:=phi(x):
Q:=psi(x):

eq1:=a11*diff(P,x,x,x,x)+a22*diff(P,x,x)+a33*P+a44*diff(Q,x,x)+a55*Q:
eq2:=a44*diff(P,x,x)+a55*P+a66*diff(Q,x,x)+a77*Q:

eq1:=0:
eq2:=0:

The boundary values for this coupled equation are:
phi(a)=sigma1,phi(-a)=sigma1,diff(P,x)(a)=0,diff(P,x)(-a)=0,psi(a)=sigma2,psi(-a)=sigma2

Now consider:

a11:=6.36463*10^(-10):
a22:=-1.22734*10^(-9):
a33:=3.48604*10^(-10):
a44:=2.94881*10^(-11):
a55:=-5.24135*10^(-11):
a66:=-1.03829*10^(-9):
a77:=4.86344*10^(-10):
when I use dsolve for deriving a good answer in this equation, there are six real roots .How can I solve it with these boundary condition?

I need to extract phi(x) and psi(x) from this coupled equation.

Thanks

 

Hello guys

I have a linear differentional equation which is in the 4th order. It is shown in the below:

P:=phi(x):
eq:=a11*diff(p,x,x,x,x)+a22*diff(p,x,x)+a33*p:
eq:=0:
where a11 and a22 and a33 are constant coefficients. The boundary value for this equation is:

phi(a)=sigma1 , phi(-a)=sigma1 , diff(p,x)(a)=0 , diff(p,x)=0

Now consider :

a11:=2.731e-10:
a22:=-1.651e-9:
a33:=3.09027e-10:
a:=35.714:
sigma1:=200e6:

when I use dsolve for deriving a good answer in this equation. there are four real roots .How can I solve it with these boundary condition?

I need to extract phi(x) from this equation.

Thanks

Hello,

I need your help to display the matrix generated by a lenear system.

The linear system is okay, well written, but  there is an error in generate matrix, I get the wrong matrix.

Thank you very much for your help.

 

test.mw

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I have a set "EQ" containing N linear equations in N unknowns. The only symbolic variables in each "EQ[i]" are the unknowns. I want to write a procedure that derives the matrices "A" and "b" where A.x=b is the same linear system stored in "EQ". In other words, I want to write the linear system in the matrix form.

Can anyone guide me through writting such a procedure?
As an example do it with the system written in the following file.

Note: This procedure will be used for large linear systems (e.g. 2000 Equations, 2000 Unknowns) so it will be important that the procedure uses the least operations required.

LinearSystem.mw

Thanks in advance.

I have a large system of linear algebraic equations that I want to solve (2005 Unknowns, 2005 Equations). I was wondering that what are the proper commands to use in maple for solving the system as fast as possible. Take a look at the files in the download link if you want to see the system of linear algebraic equations.

http://pc.cd/h79

Please provide me any suggesitons that you may think will be helpful like using other sofwares that are good in doing this work such as MATLAB or something else.


Thanks in Advance




Hi there. 

I'm kind of new to Maple and i'm trying to solve a Linear Algebra problem for my class of Linear Algebra of the course of Physics. Also, my first language is portuguese so forgive for my not-so-perfect english.

I have a (solved) linear system of 7 equations and 12 variables (A, B, C, D, E, F, G, H, I, J, K, L) that is the following:

  • A = 33 - K - L
  • B = 1 + F - J
  • C = -15 - F + J + K + L
  • D = 15 + H - K
  • E = 16 - F - H + J + K
  • G = 34 - H - J - L
  • I = 18 - J - K

Note: I'm using letters (A, B, ..., L) instead of X1X2, ..., X12 because it's easier to write it like this here and because I don't know if the Xn notation is allowed on Maple (i don't think so).

So, the system is possible but undetermined (with 5 degrees of freedom), being F, H, J, K and L the free variables.

Until here, everything's fine. The problem arises when the professor asks us for every solution of the system that satisfies the condition that all the variables (form A to L) are positive integers (A, B, C, D, E, F, G, H, I, J, K, L ϵ IN → natural numbers).

From my understanding, that gives rise to a system of linear inequalities with 12 variables and the following inequalities:

  • A = 33 - K - L > 0
  • B = 1 + F - J > 0
  • C = -15 - F + J + K + L > 0
  • D = 15 + H - K > 0
  • E = 16 - F - H + J + K > 0
  • G = 34 - H - J - L > 0
  • I = 18 - J - K > 0
  • > 0
  • > 0
  • > 0
  • > 0
  • > 0                            (and A,B,C,D,E,F,G,H,I,J,K,L ϵ IN)



After some research, i found that a possible way to solve this type of system of linear inequalities is trough a method of elimination (analog to Gauss-Jordan's elimination method for systems of linear equations) named Fourier-Motzkin. But it's hardwork and i wanted to do it on the computer. After some research, i came across with the following Maple command:

SolveTools[Inequality][LinearMultivariateSystem]

http://www.maplesoft.com/support/help/Maple/view.aspx?path=SolveTools%2fInequality%2fLinearMultivariateSystem

So, I tried to use that command to solve my system, with the following result (or non-result):

with(SolveTools[Inequality]);
LinearMultivariateSystem({F > 0, H > 0, J > 0, K > 0, L > 0, 1+F-J > 0, 15+H-K > 0, 18-J-K > 0, 33-K-L > 0, 34-H-J-L > 0, -15-F+J+K+L > 0, 16-F-H+J+K > 0}, [F, H, J, K, L]);

Error, (in SolveTools:-Inequality:-Piecewise) piecewise takes at least 2 parameters


So, i really need help solving this as the professor told us that the first one to solve would win a book, eheh. I don't know what I'm doing wrong. Maybe this Maple command is not made for 12 variables? Or maybe i'm just writing something on a wrong form. I've never used Maple before so i can be doing something really stupid without knowing it.

I would really apreciate an answer, as my only goal as a future physicist is to unveil the secrets of the Cosmos to us all.

Thank you again.

Miguel Jesus





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