restart; with(plots);
G := 1; M := .1; R := 1; P := .72; alpha := .1; phi := 1; K := 1; n := 2; beta := 1;
                               1
                              0.1
                               1
                              0.72
                              0.1
                               1
                               1
                               2
                               1
ode1 := {(1+(4/3)*R)*(diff(theta(x), x, x))+(1/2)*P*f(x)*(diff(theta(x), x))+alpha*theta(x) = 0, n*(diff(f(x), x, x))^(n-1)*(diff(f(x), x, x, x))+f(x)*(diff(f(x), x, x))/(n+1)+G*theta(x)-M*(diff(f(x), x)) = 0, f(0) = 0, theta(10) = 0, (D(f))(0) = beta*K*((D@@2)(f))(0), (D(f))(10) = 1, (D(theta))(0) = -phi*(1-theta(0))};
 /7  d  / d          \                     / d          \
{ - --- |--- theta(x)| + 0.3600000000 f(x) |--- theta(x)|
 \3  dx \ dx         /                     \ dx         /

                         / d  / d      \\ / d  / d  / d      \\\
   + 0.1 theta(x) = 0, 2 |--- |--- f(x)|| |--- |--- |--- f(x)|||
                         \ dx \ dx     // \ dx \ dx \ dx     ///

     1      / d  / d      \\                  / d      \      
   + - f(x) |--- |--- f(x)|| + theta(x) - 0.1 |--- f(x)| = 0,
     3      \ dx \ dx     //                  \ dx     /      

  f(0) = 0, theta(10) = 0, D(f)(0) = @@(D, 2)(f)(0),

                                           \
  D(f)(10) = 1, D(theta)(0) = -1 + theta(0) }
                                           /
dsol := dsolve(ode1, numeric, method = bvp[midrich], range = 0 .. 10);
Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

I try to get real solutions for a PDE, i.e. real-valued functions depending on real variables. Maple computer complex solutions, i.e. complex-valued functions depending on complex variables.

Here is the example in question: (the four function f1, f2, f3, f4 depend on the four unknowns lam, mu, l, m)

`assuming`([pdsolve([diff(f2(lam, mu, l, m), m)-(diff(f1(lam, mu, l, m), l))-(diff(f4(lam, mu, l, m), mu))+diff(f3(lam, mu, l, m), lam) = 0, diff(f1(lam, mu, l, m), m)+diff(f2(lam, mu, l, m), l)-(diff(f3(lam, mu, l, m), mu))-(diff(f4(lam, mu, l, m), lam)) = 0])], [real])

How can I solve my problem and receive only real solutions to my PDE?

A similar problem had been posted before (see here), but I can only find a cached version of the post where no answers are displayed.

Hi,

I would like to control the extents of my 3D parametric plot. Increasing the grid creates too many gridlines and I just get a black plot  (and I still don't get the extent in the y-coordinate that I want).

Any suggestions how I might be able to get this plot from -360 to 0 and -20 to 60 completely filled in? (see attached workbook).

Any suggestions on how to control the gridlines?

An idea of what I am trying to do...I want to plot argument(z/(1+z)) vs. argument(z)*180/pi vs. 20*log10(abs(z)) with contours of argument(z/(1+z)) and 20*log10(abs(z/(1+z))
This is a 3D plot of the output phase of a Nichol's Chart (with the output contours of the Nichol's chart).

Thanks.

phaseplot.mw

Hello,

I need a little help...

what I want to do, if i have 3 equations  with multiple variables and i want to get derivative of some of these variables wrt other variables while setting others as constants

here in the example

1st i thought the last equation should have partial m / partial f ... how can i get that

2nd if ,another problem, i wanted to set z as a constant so it won't consider getting its derivative, how do i get that

diff_test.mw

Download diff_test.m

hope i was clear in my explanation. thank you

I am getting this error for almost everything that i write in maple today, and i simply have no idea what causes it or what it means

Download WTF_ERROR.mw

i have a function,when using fsolve to solve it, it has two roots. when i substitute it into the main function, it has some residual and it is not exactly 0. how should i remove the residual ? i do not want to use "solve" command and i should use "fsolve" command. tnx in advance

Download problem.mw

Hello,

So my questions is fairly simple but I am not sure if Maple can do this. I want to create a Matrix full of partial derivatives (Jacobian), but computing this Jacobian is maxing out my RAM. So I would like to create each row (or column) of the Jacobian seperately and save each row (or column) in a Matrix that has already been saved to a file. Basically I would like to store values in a file (in a loop) without overwriting the file.

hey

not from a ready-made example from a module

Hello,
Can i un a maple program in console mode (example, cmd of MS-DOS), by command line?. I ask this, beacause it would take a lot less time to execute.

Regards

Hi every body:

I have to obtain A_max where is the maximum value of the f(t) function at steady state but at first i don't know steady sate what's the mean and the second i don't know how to obtain it with maple. help me plz. tnx. 

f:=(t)->A*sin(x*t)

A := -6000.*x^3*((5.925123867*10^87*I)*x+5.830850605*10^88*x^2+1.752916719*10^90)/((4.241561702*10^89*I)*x^4-2.669934485*10^90*x^5-(3.812926555*10^90*I)*x^2+7.038145625*10^91*x^3+3.174301659*10^89*I-8.376628660*10^90*x)

Sin.mw

I am looking for advice as to avoiding or identifying what may elude to the cause of the error "Error, (in simplify/do) invalid simplification command" in circumstances where i have simply enclosed an expression with simplify(expression), and in most cases an error is not returned.

Thankyou in advance

Dear Maple users

I have been investigating the one-dimensional Wave Equation for the vibrating string with fixed endpoints. Before trying to use Maple for a solution, I surfed on Google and stumbled upon a solution given in a GeoGebra animation:

https://www.geogebra.org/m/eKkFV8uz

I succeded in making a similar animation in Maple. See the attached Maple file: The last line is out-commented in order for the file not to be too big (saving many frames...). Remove the # and recalculate, select the animation object and eventually resize it. Then hit the Play Button in the Toolbar. It should work very much like the animation above. 

Now my question: I assume the numerical solution is solved using the Finite Difference Scheme in the background? How do I receive the numerical data, which lies behind the animation? Is it possible to evaluate the solution at specific (x,t) points?

I am quite impressed that GeoGebra can solve this PDE, by the way!

Regards,

Erik

Wave_Equation_-_vibrating_string2.mw

How to 'Test Relation' the Euler Product formula in Maple?

Euler product formula in Maple:

I often do "Test -> Relation" from the right-click context menu in Maple to verify equations as I enter them.

When I do that for the above Euler Product "formula", it says it is false.  I know it is because I need to further add that s > 1.

 However, I am not sure how to enter the further constraint that s must be greater than 1 (s > 1) so that Maple recognizes that before Testing the Ralation of the Euler Product equation I entered.  What is the syntax for entering that further constraint of s > 1?

Dear Users!

I want to simple the Gamma function occures in a matrix. I need the simpliest form of this matrix. If there is some thing common in all entries take it common. Thanks

Matrix(6, 6, {(1, 1) = 2*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (2, 1) = (1/2)*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (2, 2) = (1/4)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(GAMMA(alpha+1/2)^3*alpha^3*(alpha+1)^3*GAMMA(alpha)^3)*Pi^(1/4)/((2*alpha+3)*(1+2*alpha)*GAMMA(alpha+1/2)^2*alpha^2*(alpha+1)^2*GAMMA(alpha)^2), (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (3, 1) = (1/16)*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(GAMMA(alpha+1/2)^2*alpha*(alpha+1)*(1+2*alpha)*GAMMA(alpha)), (3, 2) = (1/8)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(GAMMA(alpha+1/2)^3*alpha^3*(alpha+1)^3*GAMMA(alpha)^3)*Pi^(1/4)/((2*alpha+3)*(1+2*alpha)*GAMMA(alpha+1/2)^2*alpha^2*(alpha+1)^2*GAMMA(alpha)^2), (3, 3) = (1/32)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(alpha^3*GAMMA(alpha+3/2)^3*(2+alpha)^3*GAMMA(alpha)^3)*Pi^(1/4)/((alpha+1)*(2*alpha+3)*alpha^2*GAMMA(alpha+3/2)^2*(2+alpha)^2*GAMMA(alpha)^2), (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 2*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (4, 5) = 0, (4, 6) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = (3/2)*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (5, 5) = (1/4)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(GAMMA(alpha+1/2)^3*alpha^3*(alpha+1)^3*GAMMA(alpha)^3)*Pi^(1/4)/((2*alpha+3)*(1+2*alpha)*GAMMA(alpha+1/2)^2*alpha^2*(alpha+1)^2*GAMMA(alpha)^2), (5, 6) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = (1/16)*(18*alpha+19)*GAMMA(alpha+5/2)*Pi^(1/4)*sqrt(GAMMA(alpha+1)*GAMMA(alpha+1/2)^3)/(alpha*(alpha+1)*(2*alpha+3)*(1+2*alpha)*GAMMA(alpha)*GAMMA(alpha+1/2)^2), (6, 5) = (3/8)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(GAMMA(alpha+1/2)^3*alpha^3*(alpha+1)^3*GAMMA(alpha)^3)*Pi^(1/4)/((2*alpha+3)*(1+2*alpha)*GAMMA(alpha+1/2)^2*alpha^2*(alpha+1)^2*GAMMA(alpha)^2), (6, 6) = (1/32)*GAMMA(alpha+5/2)*sqrt(2)*sqrt(alpha^3*GAMMA(alpha+3/2)^3*(2+alpha)^3*GAMMA(alpha)^3)*Pi^(1/4)/((alpha+1)*(2*alpha+3)*alpha^2*GAMMA(alpha+3/2)^2*(2+alpha)^2*GAMMA(alpha)^2)})