## How to olve system of Non linear equations...

Hi,

I need to solve system of 6 non linear equations.

Down here you can see the code I wrote and at the end used to fsolve function, and it is not running. I get an error about the const 'V': Error, (in fsolve) V is in the equation, and is not solved for.

What is the right way to solve this system?

Thank you very much!

omega1 := 1.562;
omega2 := 2.449;
omega3 := 3.325;
y1 := c1*sin(omega1*t+phi1)+c2*sin(omega2*t+phi2)+c3*sin(omega3*t+phi3);

y2 := .1019*c1*sin(omega1*t+phi1)+.75*c2*sin(omega2*t+phi2)+.4608*c3*sin(omega3*t+phi3);

y3 := .407*c1*sin(omega1*t+phi1)+(0*c2)*sin(omega2*t+phi2)+1.844*c3*sin(omega3*t+phi3);

eq1 := subs(t = 0, y1) = 0;

eq2 := subs(t = 0, y2) = 0;

eq3 := subs(t = 0, y3) = 0;

eq4 := subs(t = 0, diff(y1, t)) = V;
eq5 := subs(t = 0, diff(y2, t)) = 0;
eq6 := subs(t = 0, diff(y3, t)) = 0;

eqs := [eq1, eq2, eq3, eq4, eq5, eq6];

vars := [c1, c2, c3, phi1, phi2, phi3];

fsolve({eq1, eq2, eq3, eq4, eq5, eq6}, {c1, c2, c3, phi1, phi2, phi3});

## Need convergent solution...

Dear, I am facing the problem for solvin the attached file. Solution obtained for L=1 successfully but i need the solution for large value of L e.g., L =10. Please find the attachement and fix the problem. I am waiting positive response. Thanks in advance.

Help.mw

## Solution of system of ODEs...

Hello

Dear I want to solve the system of ODEs in attached file for different values of m1 i.e., 3,4,5 how I will use the value of m1 in dsolve. I am waiting your positive response thanks in advance.

Help.mw

## Need numerical solution of PDE...

Dears

Hope you would be fine. I want to solve the following PDEs by numerically for v[nf]=alpha[nf]=Ec=mu[nf]=C=1 and Pr=6.2

Eq1 := diff(u(x, t), t) = v[nf]*(diff(u(x, t), x, x));

Eq2 := diff(u(x, t), t) = alpha[nf]*(diff(theta(x, t), x, x))/Pr+Ec*mu[nf]*C*(diff(u(x, t), x))^2;

ICs := u(x, 0) = 0, theta(x, 0);

BCs := u(0, t) = 1, theta(0, t) = 1, u(10, t) = 0, theta(10, t) = 0;

and find the values of (diff(u(0, t), x))/(1-phi)^2.5 for different values of phi. Thanks in advace

With my best regards and sincerely.

School of Mathematical Sciences
Peking University, Beijing, China

## how must i write this formula?...

any idea for my problem?

> k1 := sum(X[h, t], t = 1 .. 23) >= 9;
9 <= X[h, 1] + X[h, 2] + X[h, 3] + X[h, 4] + X[h, 5] + X[h, 6]

+ X[h, 7] + X[h, 8] + X[h, 9] + X[h, 10] + X[h, 11] + X[h, 12]

+ X[h, 13] + X[h, 14] + X[h, 15] + X[h, 16] + X[h, 17]

+ X[h, 18] + X[h, 19] + X[h, 20] + X[h, 21] + X[h, 22]

+ X[h, 23], h = 1 .. 6

why 'h' still 'h'. from my textbooks the formula must be like this :

## How to define function with (conditions, interval,...

how will i go about solving this problem, i want to return somthing like this (this anwser is from another function that did not contain sin, and therefor did not gave me problems).

## Coordinates of a point...

I've made a system of two equations:

eq1:= x^2+y^2=0.314

eq2:= y=0.05180967688x

The first is a circle while the second is a line. I use the command fsolve in order to get the intersection and i get:

{x=0.5596,y=0.02899}

I need to use these results as the coordinates of a pointplot, how can i do it? Is there a way to isolate x and y?

Thanks

## plotting for second derivative for y=0...

yVal := 0.01

xVal := 0.01

p8 := plot([fdiff(('rhs')((pds:-value(f(x, y)))(x, yVal)[3]), [y, y], x = z)], z = 0 .. 20, color = [red])

I cant seem to plot the graph for yVal, but if I were to switch it around to (xVal,y), the graph works perfectly. How should I input the code such that I can obtain the f''(x,0) graph.

Any help will be greatly appreciated :) thanks

fyp3.mw

## Defining and Plotting Functions in Maple...

hello,

Given f(x)=2x^2-4x, how do I define and plot the functions f(x), 2f(x), 4f(x), -f(x) and -4f(x) in maple 15?

Thank You.

## The distance from the point to the surface

by: Maple 15

The distance from the point to the surface easily calculated using the NLPSolve of Optimization package. If the point is not special, we will find for it a point on the surface, the distance between these two points is the shortest between the selected point and the surface.
Two examples:  the implicit surface and the parametric surface.
To test, we restore the normals from the  calculated  points (red) by using analytical equations.
DISTANCE_TO_SURFACE.mw

## plotting a second derivative graph ...

I can't seem to plot the second derivative graph for f'' versus y. Is it possible to use the fdiff command twice in a line?

Open to all opinions. Any help would be greatly appreciated :)

fyp3.mw

## Rolling without slipping on a non-orientable surfa...

by: Maple 15

The Möbius strip  Mobius_strip_rolling.mw

Variants :

The line and the curve on the surface.

## How do I solve a system with more equations than v...

Hi everyone.

I'm using Maple 15 to try to give random values to a matrix with some columns fixed, the problem is that it has to be unitary, so I managed to create a system of equations (with 36 linear equations and 24 variables) which should give me the information i require.

I have been trying with fsolve, etc. but i haven't been able to solve it yet, as I usually get the error: "Error, (in fsolve) number of equations, 36, does not match number of variables, 24"

Is there any way to find out which equations are neccesary and get rid of the rest of them? Or can Maple give ramdon values to some of the variables and calculate the others?

## Convert Peano curve into a function...

Hi!

I have seen th following procedure to compute the image of the points of [0,1] under the so called Peano space-filling curve (sorry, I have to pasted the code in "text plane" mode):

P[0] := (x, y) -> ((1/3)*y, (1/3)*x);

P[1] := (x, y) -> (-(1/3)*x+1/3, (1/3)*y+1/3);

P[2] := (x, y) -> ((1/3)*x, (1/3)*y+2/3);

P[3] := (x, y) -> ((1/3)*x+1/3, -(1/3)*y+1);

P[4] := (x, y) -> (2/3-(1/3)*y, 2/3-(1/3)*x);

P[5] := (x, y) -> ( (1/3)*x+1/3, 1/3-(1/3)*y));

P[6] := (x, y) -> (1/3)*x+2/3, (1/3)*y);

P[7] := (x, y) -> (-(1/3)*x+1, (1/3)*y+1/3);

P[8] := (x, y) -> ((1/3)*x+2/3, (1/3)*y+2/3);

peano := proc (t::numeric, depth::integer)

local q, r; global P;

if depth = 0 then return 0, 0 end if;

q := floor(9*t); r := 9*t-q;

return P[q](peano(r, depth-1))

end proc;

Now, I need to use the procedure "peanofun" as a function. For instance, if we define f:=(x,y)->x+y, I need to use (plot, compute, etc) for instance, the function f(peanofun(t,5))

Can you help me with this issue, please?

## run code for plot the region...

can anyone run my code?
please do it and send it for me.
thanks.

restart;
with(plottools): with(LinearAlgebra): with(plots):
ode := `assuming`([diff(Y(X), `\$`(X, 2))+2*alpha*(diff(Y(X), X))+beta^2*Y(X) = 0], [alpha >= 0, beta >= 0, alpha+beta > 0]):
F := unapply(solve(subs({X = x, Y(X) = y, diff(Y(X), X) = yp, diff(Y(X), `\$`(X, 2)) = yz}, ode), yz), x, y, yp):
Fp := unapply(solve(subs({X = x, Y(X) = y, diff(Y(X), X) = yp, diff(Y(X), `\$`(X, 2)) = yz, diff(Y(X), `\$`(X, 3)) = yt}, diff(ode, X)), yt), x, y, yp, yz):
Ni := seq(i, i = 0 .. 9), 15, 20:
for ni in Ni do
print(ni);
st := time[real]();
f[0, ni] := F(x[0], y[0, ni], yp[0, ni]);
fp[0, ni] := Fp(x[0], y[0, ni], yp[0, ni], f[0, ni]);
f[1, ni] := F(x[1], y[1, ni], yp[1, ni]);
fp[1, ni] := Fp(x[1], y[1, ni], yp[1, ni], f[1, ni]);
y[2, 0] := y[0, ni]+2*h*yp[0, ni]+(6/5)*f[0, ni]*h^2+(4/15)*fp[0, ni]*h^3+(4/5)*f[1, ni]*h^2+(4/15)*fp[1, ni]*h^3;
yp[2, 0] := yp[0, ni]+2*f[0, ni]*h+(2/3)*fp[0, ni]*h^2+(4/3)*fp[1, ni]*h^2;
for j to ni do
f[2, j-1] := F(x[2], y[2, j-1], yp[2, j-1]);
fp[2, j-1] := Fp(x[2], y[2, j-1], yp[2, j-1], f[2, j-1]);
y[2, j] := y[1, ni]+h*yp[1, ni]+(7/20)*f[1, ni]*h^2+(1/20)*fp[1, ni]*h^3+(3/20)*f[2, j-1]*h^2-(1/30)*fp[2, j-1]*h^3;
yp[2, j] := yp[1, ni]+(1/2)*f[1, ni]*h+(1/12)*fp[1, ni]*h^2+(1/2)*f[2, j-1]*h-(1/12)*fp[2, j-1]*h^2;
end do:
Ms := Matrix(4, 4); Ms[1, 3] := 1; Ms[2, 4] := 1;
y[2, ni] := collect(algsubs(h*alpha = H1, expand(algsubs(h*beta = H2, expand(y[2, ni])))), {y[0, ni], y[1, ni], yp[0, ni], yp[1, ni]});
Ms[3, 1] := coeff(y[2, ni], y[0, ni]);
Ms[3, 2] := coeff(y[2, ni], yp[0, ni])/h;
Ms[3, 3] := coeff(y[2, ni], y[1, ni]);
Ms[3, 4] := coeff(y[2, ni], yp[1, ni])/h;
hyp[2, ni] := collect(algsubs(h*alpha = H1, expand(algsubs(h*beta = H2, expand(h*yp[2, ni])))), {y[0, ni], y[1, ni], yp[0, ni], yp[1, ni]});
Ms[4, 1] := coeff(hyp[2, ni], y[0, ni]);
Ms[4, 2] := coeff(hyp[2, ni], yp[0, ni])/h;
Ms[4, 3] := coeff(hyp[2, ni], y[1, ni]);
Ms[4, 4] := coeff(hyp[2, ni], yp[1, ni])/h;
sol := Eigenvalues(Ms);
print(time[real]()-st);
st := time[real]();
SR[ni, 1] := implicitplot(max(seq(abs(sol[ii]), ii = 1 .. numelems(sol))) <= 1, H1 = 0 .. 3, H2 = 0 .. 3, filledregions, gridrefine = 3, axes = Boxed, view = [-2 .. 3, -3 .. 3], labels = [H[1], H[2]], labeldirections = ["horizontal", "vertical"]);
SR[ni, 2] := implicitplot(max(seq(abs(sol[ii]), ii = 1 .. numelems(sol))) <= 1, H1 = -2 .. 3, H2 = -2 .. 3, gridrefine = 3, axes = Boxed, view = [-2 .. 3, -3 .. 3], labels = [H[1], H[2]], labeldirections = ["horizontal", "vertical"]);
print(time[real]()-st);
end do;
for i in Ni do
i;
display({SR[i, 1], SR[i, 2], line([-1, 0], [3, 0], color = red, linestyle = dash), line([0, -3], [0, 3], color = red, linestyle = dash)});
end do;
display({seq(SR[i, 2], i = 0 .. Ni)});

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