Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

Non-Linear.mw

Hi, I have here a interesting non-linear system.

If I attempt to solve it using some specific form of the non-linear equations (form X*Y=Z) of the system, Maple (Verison 18) finds a solution.

But, if I replace some of them by some other forms (like form Y=Z/X), fsolve fails.

I usually use the non-quotient form. But is there any way to guide or configure fsolve to reach a solution?
I set up some of the regular options: placing a seed close to the solution, indicating intervals of possible solutions; but none of that works if I do not set up the non-quotient form of the equations. In some cases, fsolve does not reach a solution at all, no matter the form of the equations.

In the file, the equations that are causing the isssue are the last 3, those who start with the variable f1,f2 and f3.
I ran the system twice with both cases: non-quotient form and quotient form.

Thanks for your attention! 

Given a set (list) of PDE, is there a way to search all possible solution sets? For instance, pdsolve will output the solution

{_eta[0](t, x) = 0, _xi[t](t, x, u) = _C1, _xi[x](t, x, u) = _C2, eta[1](t, x) = 0}

for the list of PDEs below. But I am aware that there is another solution different from the above, is there way to seek these other solutions?

 

[alpha*u^2*(diff(eta[1](t, x), t))+alpha*u*(diff(_eta[0](t, x), t))-u*(diff(eta[1](t, x), t))-u*(diff(eta[1](t, x), x))+u*(diff(eta[1](t, x), x, x, t))-(diff(_eta[0](t, x), x))-(diff(_eta[0](t, x), t))+diff(_eta[0](t, x), x, x, t), -(diff(_xi[x](t, x, u), u, u, u)), -(diff(_xi[t](t, x, u), x))-(diff(_xi[t](t, x, u), t)), -(diff(_xi[t](t, x, u), x, x)), -2*(diff(_xi[t](t, x, u), x, x))-(diff(_xi[x](t, x, u), x, x))+2*(diff(eta[1](t, x), x)), diff(eta[1](t, x), t)-2*(diff(_xi[x](t, x, u), x, x)), -(diff(_xi[x](t, x, u), t))*alpha*u-(diff(_xi[x](t, x, u), x, x, x))-(diff(_xi[t](t, x, u), x))+2*(diff(eta[1](t, x), x, t)), -(diff(_xi[x](t, x, u), x)), -(diff(_xi[t](t, x, u), t))*alpha*u+(diff(_xi[t](t, x, u), x))*alpha*u+(diff(_xi[x](t, x, u), x))*alpha*u+(diff(_xi[x](t, x, u), t))*alpha*u+eta[1](t, x)*alpha*u+alpha*_eta[0](t, x)+diff(_xi[t](t, x, u), t)-(diff(_xi[t](t, x, u), x, x, x))-(diff(_xi[x](t, x, u), x))-(diff(_xi[x](t, x, u), t))+diff(eta[1](t, x), x, x), -2*(diff(_xi[x](t, x, u), u)), -2*(diff(_xi[t](t, x, u), x, u)), -2*(diff(_xi[t](t, x, u), u))-(diff(_xi[x](t, x, u), u)), -(diff(_xi[t](t, x, u), u)), -(diff(_xi[t](t, x, u), u)), -5*(diff(_xi[x](t, x, u), u, u)), -(diff(_xi[t](t, x, u), u, u)), -3*(diff(_xi[t](t, x, u), x, u)), -2*(diff(_xi[x](t, x, u), u)), -(diff(_xi[t](t, x, u), u)), -(diff(_xi[t](t, x, u), u)), -2*(diff(_xi[t](t, x, u), u, u))-(diff(_xi[x](t, x, u), u, u)), -(diff(_xi[t](t, x, u), u, u, u)), -3*(diff(_xi[t](t, x, u), u, u)), -3*(diff(_xi[t](t, x, u), x, u, u)), (diff(_xi[t](t, x, u), u))*alpha*u-(diff(_xi[x](t, x, u), u))-3*(diff(_xi[t](t, x, u), x, x, u)), -2*(diff(_xi[x](t, x, u), x, u))-4*(diff(_xi[t](t, x, u), x, u)), -(diff(_xi[t](t, x, u), u))*alpha*u+(diff(_xi[x](t, x, u), u))*alpha*u+diff(_xi[t](t, x, u), u)-(diff(_xi[x](t, x, u), u)), -3*(diff(_xi[x](t, x, u), x, x, u))-(diff(_xi[t](t, x, u), u)), -7*(diff(_xi[x](t, x, u), x, u)), -3*(diff(_xi[x](t, x, u), x, u, u))]

Could you Please Help me,the Maple code for Plot this equations in any Numerical Method

restart

with(PDETools, declare):

with(LinearAlgebra):

with(PolynomialIdeals):

with(plots):

declare(f(x));

f(x)*`will now be displayed as`*f

(1)

eq1 := diff(f(x), x, x, x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cosω`+f(x)*`sinω`)*(diff(f(x), x, x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[fl])*lambda[T]*theta = 0;

diff(diff(diff(f(x), x), x), x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cosω`+f(x)*`sinω`)*(diff(diff(f(x), x), x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`ρβ`[s]/`ρβ`[fl])*lambda[T]*theta = 0

(2)

eq2 := K[nf]*(diff(theta(x), x, x))/K[f]+(1/2)*Pr*(eta*`cosω`+f*`sinω`)*(diff(theta(x), x)) = 0;

K[nf]*(diff(diff(theta(x), x), x))/K[f]+(1/2)*Pr*(eta*`cosω`+f*`sinω`)*(diff(theta(x), x)) = 0

(3)

bcs := F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0;

F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0

(4)

a1 := [M = 1, alpha = 0, phi = 0.5e-1, `cosω` = 1, `sinω` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, `ρβ`[fl] = 20939.1, K[nf] = .6842, eta = 0];

[M = 1, alpha = 0, phi = 0.5e-1, `cosω` = 1, `sinω` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, `ρβ`[fl] = 20939.1, K[nf] = .6842, eta = 0]

 

[Pr = 6.2, M = 1, phi = 0.5e-1, `cosω` = 1, `sinω` = 1, sin(alpha) = 0, lambda[T] = 0, `ρβ`[fl] = 20939.1, K[nf] = .6842, K[f] = .613, eta = 0]

(5)

b1 := subs(a1, eq1);

diff(diff(diff(f(x), x), x), x)+.5325197465*f(x)*(diff(diff(f(x), x), x)) = 0

(6)

c1 := subs(a2, eq2);

1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x)) = 0

(7)

d1 := dsolve({b1, bcs}, {bcs, c1}, numeric); d1(0)

Error, (in dsolve/numeric/process_input) invalid argument: {1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x)) = 0, F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0}

 

d1(0)

(8)

``

Download  Numerical Method.mw

Why solutions (5) and (6) are different? The solution (5) is obtained by putting f=0 of the series, while (6) is the result by taking limit at f->0. 

check.mw

hallo evert body please how i do calculate this integral

in maple 18

ttp.pdf

int_{0}^{2\pi}(\cos^{i}(\theta)-\cos^{i+2}(\theta))d\theta

Please I will like to know if there exists any command to isolate the known regular mathematical functions from an expression. For example, given the equation 

I need a means of isolating (ex & sin(v)) from the above expression

Thanks

How can we export image with minimum size? I plot the solution and then export the image as an .eps file. But when I try to generate the generate the pdf file on Latex, the file size is too large. But when I plot the solutions on Matlab and export the images as .eps file, then Latex generate pdf file with samll size. Why Maple generate images of large sizes?

solution.mw

I am using the Calculus Study Guide and the mathematical notation is half Maple notation and then half typeset notation. I have tried to tweak with Tools>Options>Display settings but it stays the same

For example:

{a[n]}[n = n[0]]^infinity;, where 
                             "a[n]"

 is the general term for the sequence, and 
                             "n[0]"

 is the starting index.
The notation is often shortened to {a[n]}; to save printing costs.

...and the math notation past the word "where" is in typeset notation but changed to Maple Notation when I cut and pasted.

Thank You in advance.

Please how can I define two sequences in a procedure with two arguments?

  ans:= Array([seq( [j, doCalc(j, u)], j=-2..0, 0.006, u=1..334)]):

The procedure is doCalc(j,u)  and I received this error: invalid input: seq expects between 1 and 3 arguments, but received 4

Find attached my complete code.Seq_Proc.mw

How to replace 7th-row(second last) of the matrix H116 (see eq. (14)) with the 1st-row of the matrix H16 (see eq. (15)) and create a new matrix of size same as H116?

matrixop.mw

Hi! Can anyone show me a quick example of a procedure with local and global variables?!? It seems that i'm not getting the hang of it, because i keep receiving "unable to parse" messages. 

During evaluating psi0 (see eq, (7))why we need two values of f (i.e., f,0 and f,3)? I asked one of my seniors and according to him these values are arbitrary. Can anyone explain why we need two values and why f,0 and f,3?

rwo.mw  

Hi, Maple users 

I hope you are doing well.
Here I solved one of the ode problems by dsolve.
But I am getting  "Error, invalid subscript selector" error.
Kindly do the needful to find a solution.
Thank you.

JVB.mw

 I want to plot phase portrait but i get some errors. I didn't understand errors? Can anyone help me? zuhal_faz_portresi.mw

I have been studying the solutions of the equation below using Maple and Mathematica. 

Here, I want to express the solutions for k. In Maple, the solution is imaginary. As one may see below.

On the other hand, if one solves that  exact equation with Mathematica, then one has real solutions. That is,

Based on the above, I have a few questions:

1. What is the correct solution for the first equation above? That is, are the solutions real or complex?

2. How may I obtain the real solutions, k_{1,2}, above using Maple?

Attached below you may find my mwfile with my doubts.

Mydoubts.mw

Thanks in advance.

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