Hello Everyone;

I have 2D domain meshing defined. I need to plot it like figure given at end. I need to heighlights boundry and ineer points saperately and need to mention the points on it. Domain and mesh is given in Maple file attched. Kindly guide me.

Thanks

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Hello Everyone;

Hope you are fine. I am solving system of odes using rk-4 method. For this purpose I formulate the "residual" (on maple file) which is further function of "x" and "y". With the help of discritization point further I convert "residual" into system of ode's. Then i used "sys111 := solve(odes_Combine, `~`[diff](var, t))" to simplify the system. Finnally i applied RK-1. Code is pasted and attached. This all process is for "N=4". When i increase the value of "N", number of Odes increase accordingly. With increasing value of "N" the comand "sys111 := solve(odes_Combine, `~`[diff](var, t))" taking a lot of time due to heavy computation. Is that any way to proceed without this comand for rk-1?

Question1.mw

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Hello Everyone;

Hope you are fine. Solve comand is solving Equation saperately but samultanously. Kindly guide me about this. I have uploaded and pasted the code as well. The last comand (in red color) is not working. I am waiting for the kind response.

Thanks

QuestionNo1.mw

Hello Everyone;

Hope you are fine. I am applying rk-4 and Runge-Kutta-Fehlberg method for system of odes but there is no difference in the result of these method. Can anybody guide about that for my problem. I have uploaded the code. Thanks in advance.

Question#3.mw

Hello;

Hope you are fine. Can i apply numerical scheme on maple for the following problem. This in integro-differential equation i think. Waiting for kind response.

Thanks

Hello; 

Hope you are fine. I am devolping code for rk-2 at N=8 and further comparing my results with bultin comands on rk-2 on maple. My results is not matching with maple buliton commands. I am confused and tried a lot but not able to find the mistake. I have attached code. May be i have mistake in the calculation of K_1 and K_2. Kindly guide me please. Thanks a lot in advance.

Question_(1)_Posted.mw

I want to apply rk-2 for the following system of odes. I want to know what is process of rk-2 method maple used? Is it possible that we can see the complete process maple used?

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Hello Sir
Hope you are fine. I am facing issues in integration evaluations. I have attched code and pic as well. Kindly guide me. I am waiting for your kind response.
Thanks

question.mw

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Maple (2015) fails to instanciate a Matrix with a list of elements of type string
(for instance Matrix(2, 2, ["A", "B", "C", "D"]) )

Matrix(2$2, [1$4]):    # ok
Matrix(2$2, [A$4]):    # ok

Matrix(2$2, ["A"$4]);  # not correctly understood by Maple (2015) 
Error, (in Matrix) initializer defines more columns (4) than column dimension parameter specifies (2)

Is this a bug?
Maybe something corrected in earlier versions?

I solve numerically a DAE system whose independent variable is named t and the dependent variables are d[1](t), ..., d[n](t).
I would like to to 2D or 3D plots of the solutions and color the resulting curve using a function f(...) of the remaining dependent variables.

Here is a simple example.

Download coloring.mw

How can I fix (if possible) the syntax in the command 

plot3d(SOL(s), s=0..4*Pi, colorfunc=f(s)):

???

Thanks in advance

Hello;

I am facing "Error, too many levels of recursion" in loops. kindly guide me. Thanks

1D1P.mw

(Maple 2015)

Why is m1(t) not evaluated correctly when I use a compound condition?

restart:
m2(t) = piecewise(x1(t) < c and v1(t) < 0, 1,  0);
       m2(t) = piecewise(x1(t) < e2 and v1(t) < 0, 1, 0)

m1(t) = piecewise(x1(t) = c and v1(t) > 0, 0,  1);
                           m1(t) = 1

This doesn't happen for simple conditions
 

m2(t) = piecewise(x1(t) < c, 1,  0);
m1(t) = piecewise(x1(t) = c, 0,  1);
               m2(t) = piecewise(x1(t) < c, 1, 0)
               m1(t) = piecewise(x1(t) = c, 0, 1)

TIA

Dear Users!

Hope everyone is fine here. Let me explain my problem first for this consider
diff(Y(xi), xi) = mu*(1-Y(xi)^2)
Then the derivative of a function U=u(Y(xi)) using chain rule (and expression menstiones as red) is given as,
diff(U, xi) = (diff(diff(Y, xi), Y))*U and (diff(diff(Y, xi), Y))*U = mu*(1-Y(xi)^2)*(diff(U, Y))
Similarly the second-order derivaitve of U=u(Y(xi)) using chain rule (and expression menstiones as red) is given as,
((ⅆ)^(2))/(ⅆ xi^(2))U=(ⅆ)/(ⅆ xi)(mu (1-Y^(2)(xi))*(ⅆ)/(ⅆ Y)U)=((ⅆ)/(ⅆ Y)*(ⅆ)/(ⅆ xi)Y)(mu (1-Y^(2)(xi))*(ⅆ)/(ⅆ Y)U)=(ⅆ)/(ⅆ Y)(mu^(2) (1-Y^(2)(xi))^(2)*(ⅆ)/(ⅆ Y)U)=-2 Y(xi) mu^(2) (1-Y^(2)(xi))*(ⅆ)/(ⅆ Y)U+ mu^(2) (1-Y^(2)(xi))^(2)*((ⅆ)^(2))/(ⅆ Y^(2))U;
In the similar way I want to compute the higher-order (like 5th order) derivaitve of U w.r.t. xi using the chain rule  (and expression menstiones as red) explained in above. Kindly help me soolve my problem

I am waiting for positive response.

Dear Users!

Hope you are doing well. I have a funtion give bellow:
beta[1]*exp(x*alpha[1]+y*beta[1]-z*sqrt(-alpha[1]^2-beta[1]^2))/(1+exp(x*alpha[1]+y*beta[1]-z*sqrt(-alpha[1]^2-beta[1]^2)));
For any value of alpha[1] and beta[1] the term highlighted red becomes the imaginary form. I want to separate the real and imaginary parts of this function. Kindly help me in this matter, thanks

I want to compute the series expansion of i3_r wrt (x, y, z) at point (x=y=z=0):

i2   := (x,y) -> -(1/2)*I*(exp(I*x)*(sin(x)/x)-exp(I*y)*(sin(y)/y))/(x-y):
i3_r := -(1/2)*I*(i2(y,z)-i2(y,x))/(z-x);

My first attempt was to compute this mulltiple series expansion this way:

ordre := 3:
sx := convert( series(i3_r, x, ordre), polynom);
sy := convert( series(sx  , y, ordre), polynom);
sz := convert( series(sy  , z, ordre), polynom);

But this gives me sy=sz=0 whatever the expansion order.

I then do this:

sx :=              convert(series(i3_r , x, ordre), polynom):
sy := add(map(u -> convert(series(u    , y, ordre), polynom), [op(expand(sx))])):
sz := add(map(u -> convert(series(u    , z, ordre), polynom), [op(expand(sy))]));

and obtained non zero results for both sy and sz (but are they are correct ?).

Could you explain me what happens and tell me how to find the series expansion of i3_r wrt (x, y, z) ?

TIA