MaplePrimes Questions

 

phi := sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh(Pi/(4*y))+c__4*y*sinh((1/4)*Pi*y));

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(1)

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(2)

diff((2), y);

sin((1/4)*Pi*x)*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi)

(3)

diff((3), y);

sin((1/4)*Pi*x)*((1/16)*c__1*cosh((1/4)*Pi*y)*Pi^2+(1/16)*c__3*cosh((1/4)*Pi/y)*Pi^2/y^3+(1/2)*c__4*cosh((1/4)*Pi*y)*Pi+(1/16)*c__4*y*sinh((1/4)*Pi*y)*Pi^2)

(4)

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(5)

diff((5), x);

(1/4)*cos((1/4)*Pi*x)*Pi*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(6)

diff((6), x);

-(1/16)*sin((1/4)*Pi*x)*Pi^2*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(7)

phi

sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(8)

diff((8), x);

(1/4)*cos((1/4)*Pi*x)*Pi*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))

(9)

diff((9), y);

(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi)

(10)

``

(11)

-(1/16)*Pi^2*sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y))=0;

-(1/16)*Pi^2*sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y)) = 0

(12)

eval( (12), [x = 0]);

0 = 0

(13)

-(1/16)*Pi^2*sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y)) = 0

-(1/16)*Pi^2*sin((1/4)*Pi*x)*(c__1*cosh((1/4)*Pi*y)+c__3*y*cosh((1/4)*Pi/y)+c__4*y*sinh((1/4)*Pi*y)) = 0

(14)

eval( (14), [x = 20]);

0 = 0

(15)

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((1/4)*Pi*y)+(1/16)*c__3*Pi^2*cosh((1/4)*Pi/y)/y^3+(1/2)*c__4*Pi*cosh((1/4)*Pi*y)+(1/16)*c__4*y*Pi^2*sinh((1/4)*Pi*y)) = 0

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((1/4)*Pi*y)+(1/16)*c__3*Pi^2*cosh((1/4)*Pi/y)/y^3+(1/2)*c__4*Pi*cosh((1/4)*Pi*y)+(1/16)*c__4*y*Pi^2*sinh((1/4)*Pi*y)) = 0

(16)

eval( (16), [y = 9]);

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((9/4)*Pi)+(1/11664)*c__3*Pi^2*cosh((1/36)*Pi)+(1/2)*c__4*Pi*cosh((9/4)*Pi)+(9/16)*c__4*Pi^2*sinh((9/4)*Pi)) = 0

(17)

evalf[5]( (17) );

sin(.78540*x)*(362.25*c__1+0.84938e-3*c__3+4182.6*c__4) = 0.

(18)

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((1/4)*Pi*y)+(1/16)*c__3*Pi^2*cosh((1/4)*Pi/y)/y^3+(1/2)*c__4*Pi*cosh((1/4)*Pi*y)+(1/16)*c__4*y*Pi^2*sinh((1/4)*Pi*y)) = -sin((1/4)*pi*x);

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((1/4)*Pi*y)+(1/16)*c__3*Pi^2*cosh((1/4)*Pi/y)/y^3+(1/2)*c__4*Pi*cosh((1/4)*Pi*y)+(1/16)*c__4*y*Pi^2*sinh((1/4)*Pi*y)) = -sin((1/4)*pi*x)

(19)

eval( (19), [y = -9]);

sin((1/4)*Pi*x)*((1/16)*c__1*Pi^2*cosh((9/4)*Pi)-(1/11664)*c__3*Pi^2*cosh((1/36)*Pi)+(1/2)*c__4*Pi*cosh((9/4)*Pi)+(9/16)*c__4*Pi^2*sinh((9/4)*Pi)) = -sin((1/4)*pi*x)

(20)

evalf[5]( (20) );

sin(.78540*x)*(362.25*c__1-0.84938e-3*c__3+4182.6*c__4) = -1.*sin(.25000*pi*x)

(21)

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

(22)

eval( (22), [y = 9]);

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((9/4)*Pi)*Pi+c__3*cosh((1/36)*Pi)-(1/36)*c__3*sinh((1/36)*Pi)*Pi+c__4*sinh((9/4)*Pi)+(9/4)*c__4*Pi*cosh((9/4)*Pi)) = 0

(23)

evalf[5]( (23) );

-.78540*cos(.78540*x)*(461.22*c__1+.99617*c__3+4738.2*c__4) = 0.

(24)

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0;

-(1/4)*cos((1/4)*Pi*x)*Pi*((1/4)*c__1*sinh((1/4)*Pi*y)*Pi+c__3*cosh((1/4)*Pi/y)-(1/4)*c__3*sinh((1/4)*Pi/y)*Pi/y+c__4*sinh((1/4)*Pi*y)+(1/4)*c__4*y*cosh((1/4)*Pi*y)*Pi) = 0

(25)

eval( (25), [y = -9]);

-(1/4)*cos((1/4)*Pi*x)*Pi*(-(1/4)*c__1*sinh((9/4)*Pi)*Pi+c__3*cosh((1/36)*Pi)-(1/36)*c__3*sinh((1/36)*Pi)*Pi-c__4*sinh((9/4)*Pi)-(9/4)*c__4*Pi*cosh((9/4)*Pi)) = 0

(26)

evalf[5]( (26) );

-.78540*cos(.78540*x)*(-461.22*c__1+.99617*c__3-4738.2*c__4) = 0.

(27)

s:=solve({sin(.78540*x)*(362.25*c__1+0.84938e-3*c__3+4182.6*c__4) = 0,sin(.78540*x)*(362.25*c__1-0.84938e-3*c__3+4182.6*c__4) = -1.*sin(.25000*Pi*x),-.78540*cos(.78540*x)*(461.22*c__1+.99617*c__3+4738.2*c__4) = 0,-.78540*cos(.78540*x)*(-461.22*c__1+.99617*c__3-4738.2*c__4) = 0},{c1,c2,c3,c4});

{c__1 = 0., c__3 = 0., c__4 = 0., x = 0.}, {c__1 = -10.27318850*c__4, c__3 = 0., c__4 = c__4, x = 0.}, {c__1 = -11.54616977*c__4-0.1380262250e-2, c__3 = 588.6646731, c__4 = c__4, x = -1.999995323}, {c__1 = -11.54616977*c__4-0.1380262250e-2, c__3 = 588.6646731, c__4 = c__4, x = 1.999995323}

(28)

``

 

Download analytical_case_1.mw

Dear collegues

Hope you are fine

I wrote a code to solve a system of ODEs.

The code solve the problem for higher values of parameter NBT>=5. When I decrease it to NBT=0.2, the code didnt converge. I did my best but I couldnt get the results.

I would be most grateful if you help me at this problem

The code is attached

Thank you

Final_code.mw

 

Amir

Hello all! I've just learned about Maple. My English is not very good :( I write matrix A:=L*U program. If you know it, you will understand my mind. But I received "error" from Maple. Thanks for your viewing

A=LU.mw

My_Plot.mw

Hi all,

I want to plot This attached figure in Matlab. As we know the HeunT function is not defined in Matlab. Now I want to get all the three curves Data for plotting them in Matlab. I have asked this some days ago and I got it. But now I want to get data for three curves instead of one.

 

Please help me.

There have come unwanted lines and marks . I donot know how to remove them. Using doc.block, remove block seems to be little tough to incorporate! Please enlighten me. Modified doc. is most welcome. Thanks. Ramakrishnan V 

Gaussian Elimination Method

 

 

Given*the*equations

  restartreset:

with(Student[LinearAlgebra])``

(1)
Coefficient Tanle

Equation 1

Equation 2

Equation 3

Equations

`m__1,1` := 3:
`` 

`m__2,1` := 2:
``

`m__3,1` := 1:
``

`m__1,1`*x__1+`m__1,2`*y+`m__1,3`*z = `m__1,4`; = 3*x__1+y-z = 3

`m__2,1`*x__1+`m__2,2`*y+`m__2,3`*z = `m__2,4`; = 2*x__1-8*y+z = -5

```m__3,1`*x__1+`m__3,2`*y+`m__3,3`*z = `m__3,4`; = x__1-2*y+9*z = 8

The equations in matrix form is given by

Matrix([[3, 1, -1, 3], [2, -8, 1, -5], [1, -2, 9, 8]])

(2)

The Gaussian Elimination gives the simplified natrix equation as given below:

Matrix([[3, 1, -1, 3], [0, -26/3, 5/3, -7], [0, 0, 231/26, 231/26]])

(3)

``The equations in simplified form are:

3*x+y-z = 3

(4)

-(26/3)*y+(5/3)*z = -7

(5)

(231/26)*z = 231/26

(6)

``

The aolution ia obtained by solving the above equations in reverse order

{x = 1, y = 1, z = 1}

(7)

 

``

 

Download GausianFinal15Nov2015.mwGausianFinal15Nov2015.mw

hello eveyone! sorry, my English is not very good

I writed Neville algorithm

I want to creat a table(or a matrix) Q with

example:

f:=X->2^X;

with value of X: -2,1,0,1,2

-2   1/4

-1    1/2

0    1

1    2

2     4

I want to approximate f at x=0.5 by Neville

then:   for i:=2,...,n   (that case is 5)

             for j:=2,...i

 

                  Q[i,j]=(x-X[i-j])*Q[i,j-1]-(x-X[i])*Q[i-1,j-1])/(X[i]-X[i-j])

       output(Q)

this is:

-2  1/4     0       0            0          0

-1  1/2     0.875  0           0           0

0  1         1.25   1.3475    0           0

1  2         1.5    1.4375   1.421875  0

2  4         1      1.375      1.40625  1.412109375


do you understand my mind? sorry, my English is not very good

Regards

   sunflower

hi all

i have a complex numeric like s. 

how can i calculate s

There are the complexes (C), quaternions (H or Q), octionions (O), sedenions (S) and the pathions (P). I have found the multiplication tables of them, although according to signs (+ or -) there differents at pathions. The important question is that How can I multiply two bases, i_n and i_m of higher dimensions, like in the routions or in the voudions?

Should I xor the indexes of the bases? Like this way: i_1 * i_2 = i_(1^2) = i_3

What is about the signs?

Hello,

I would like to plot an non linear oscillator.

The equations are the following:

r:=sqrt((x(t)/a)^2+(z(t)/b)^2);
eqx:=diff(x(t),t)=alpha*(1-r^2)*x+wa/b*z(t);
eqz:=diff(z(t),t)=beta*(1-r^2)*y+wb/a*x(t);
EqSys:=[eqx,eqz];

The constants are the following :

alpha:=1:
beta:=1:
a=0.4:
b=0.2:
w=1:

I didn't manage with Deplots. May you help me to plot this oscillator?

Thank a lot for your help and ideas

I'm trying to solve the differential equation.

Eq := diff(y(x), x, x) = -(x^2+1)*y(x)+K;

dsolve({Eq, y(-1) = 0, y(1) = 0}, y(x));

But this not work very well.

Best Regards,

 

I am using Maple 15, and before that Maple 8 and Maple 13. While using the versions 13 and 15, 

I come across with this problem; I cannot copy an output and use it as input. In Maple 8, I was able to do this but in 

these improved versions, it seems that it is not possible. Is there a way to solve this problem? I saw some answers about this

problem suggesting to change launch.ini file. But I could not apply this suggestion, since it is not permitted by the system. 

pde1 := 4*x*(diff(u(x, y), x))-2.*u(x, y)-y*(diff(u(x, y), y))+diff(v(x, y), y) = 0; pde2 := 4.*x.u(x, y).(diff(u(x, y), x))+(v(x, y)-y.u(x, y)).(diff(u(x, y), y))+2.*u(x, y)^2 = diff(u(x, y), `$`(y, 2))+theta(x, y); pde3 := 8.*u(x, y).theta(x, y)+4.*x.u(x, y).(diff(theta(x, y), x))+(v(x, y)+y.u(x, y)).(diff(theta(x, y), y)) = 1/100.(diff(theta(x, y), `$`(y, 2))); bc1 := u(x, 0) = 0, v(x, 0) = 0, theta(x, 0) = 1; bc2 := u(0, y) = 0, v(0, y) = 0, theta(0, y) = 0; bc3 := u(x, 20) = 0, theta(x, 20) = 0hello dear
how can i solve this three couplde pde?please help me

The word command for square root is sqrt.  What is the word command for square?  How to square all the values in a list?

 

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