Maple 18 Questions and Posts

Maple Code to solve Perturbation Iteration Solutio...

Asked by: abiodunowoyemi9 30

January 14 2023

1 0

Hi,

May I please get a Maple code to solve the below Perturbation Iteration Solutions for Volterra Integral Equations?

I shall be very much grateful if I can get the Maple Code.

And possible plotting

Thanks

Simplification of polynomials on radicals....

Asked by: ContrapuntoBrowniano 40

November 28 2022

0 1

Hi! I need to simplify a polynomial over an arbitrary field F on a radical variable ν, such that for some power j, ν is in F.

the polynomial takes the form:

k₀+a₁ν^1/j+...+a_nν^n/j

but, since ν^j is in F, this divides every element νⁱ^/jinto a cotient group of order j, so this can be rewritten as a radical extension of F, in the form:

k₁+(a₁+...)ν^1/j+...+(a_k+...)ν⁽^j-1)/j

where k_i, a_i are in F. I feel like this is a very straightforward technique for handwritten algebra, but i can't see a command for this on Maple 18. Nor the simplify(..., radicals) Or the combine(...,radicals) seems to help here. Maybe there's an special command for this? Must i do it myself? Please, any help is aprecciated.

"unable to compute solution for t>HFloat(0.0):" Ho...

Asked by: 666 jvbasha 130

November 17 2022

0 7

Hi maple users

I am working with the PDE solver.

i am receiving a following error

"unable to compute solution for t>HFloat(0.0):"

Kindly do the needful how to rectify this error.

dumm.mw

Extracting matrix of 208x2...

Asked by: ijuptilk 100

October 13 2022

0 2

Please how can I use getdata to extract only 200x2 of 208x2 matrix from maple to excel.

For instance I have:

Q:= ( seq( seq( plottools:-getdata(ans1[s1,3])[j,3],j=1..3), s1=1));

It returns 208x2, 200x2 200x2 matrices and I can't extract it using

`<|>`( seq( seq( plottools:-getdata(ans1[s1,3])[j,3],j=1..3), s1=1));

because the matrices have different dimension. Please, how can make 208x2 matrix to 200x2?

Contour with different colors such the region abov...

Asked by: ijuptilk 100

September 20 2022

1 0

I want to change the colors of a contour such that the region above zero is represented by a different color instead of yellow color, and that the colors for conts <0 are one set of colors (maybe yellow to red), and the area for which conts >0 is one color which is very different from the others (so maybe white).

Case4Contour.mw

Bifurcation of SEIR...

Asked by: ijuptilk 100

July 13 2022

0 2

Hi,

Please can someone help me with a sample code for bifurcation? You can use parameter values for the parameters. I'm using maple 18. Below is my model:

>

restart:

>	f__1 := Delta -(psi + mu)*S(t);

(1)

>	f__2 := psiS(t) -(delta + mu)E(t);

(2)

>	f__3 := DeltaE(t) -(gamma+gamma__1 + mu)X(t);

(3)

>	f__4 := gamma__1X(t)-(eta + xi + mu)H(t);

(4)

>	f__5 := xiH(t) - muR(t);

(5)

>	f__6 := gammaX(t)-etaH(t) - d*D(t);

(6)

>	f__7 := bD(t) - bB(t);

(7)

>	f__8 := phi__p + sigmaX(t)+eta__1H(t) +d__1D(t)+ b__1B(t) - alpha*P(t);

(8)

Download Bifurcation.mw

PDETools:-pdsolve other solutions...

Asked by: Chorux 60

July 08 2022

1 1

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))]

recursive differentiation...

Asked by: Chorux 60

April 25 2022

2 1

I am trying to develop a recursive code to the above equations. Note, U,X&Y are multivariate functions (in this case bivariate functions of (x,y)) i.e. U=U(x,y), X=X(x,y) etc.

Is our substitution is Ok...

Asked by: bashar27 55

April 08 2022

0 0

restart;
u := (H(x, t, z)+sqrt(R))*exp(I*R*x);
/ (1/2)\
\H(x, t, z) + R / exp(I R x)

I*(Diff(u, z))+Diff(u, `$`(x, 2))+Diff(u, `$`(t, 2))+(abs(u)*abs(u))*u-((abs(u)*abs(u))*abs(u)*abs(u))*u;
/ d // (1/2)\ \\
I |--- \\H(x, t, z) + R / exp(I R x)/|
\ dz /

/ 2 \
|d // (1/2)\ \|
+ |-- \\H(x, t, z) + R / exp(I R x)/|
\ /

/ 2 \
|d // (1/2)\ \| 2
+ |-- \\H(x, t, z) + R / exp(I R x)/| + (exp(-Im(R x)))
\ /

2
| (1/2)| / (1/2)\
|H(x, t, z) + R | \H(x, t, z) + R / exp(I R x) -

4
4 | (1/2)| / (1/2)\
(exp(-Im(R x))) |H(x, t, z) + R | \H(x, t, z) + R /

exp(I R x)
value(%);
/ d \ / d / d \\
I |--- H(x, t, z)| exp(I R x) + |--- |--- H(x, t, z)|| exp(I R x)
\ dz / \ dx \ dx //

/ d \
+ 2 I |--- H(x, t, z)| R exp(I R x)
\ dx /

/ (1/2)\ 2
- \H(x, t, z) + R / R exp(I R x)

/ d / d \\ 2
+ |--- |--- H(x, t, z)|| exp(I R x) + (exp(-Im(R x)))
\ dt \ dt //

2
| (1/2)| / (1/2)\
|H(x, t, z) + R | \H(x, t, z) + R / exp(I R x) -

4
4 | (1/2)| / (1/2)\
(exp(-Im(R x))) |H(x, t, z) + R | \H(x, t, z) + R /

exp(I R x)
simplify(%);
/ d \ / d / d \\
I |--- H(x, t, z)| exp(I R x) + |--- |--- H(x, t, z)|| exp(I R x)
\ dz / \ dx \ dx //

/ d \ 2
+ 2 I |--- H(x, t, z)| R exp(I R x) - R exp(I R x) H(x, t, z)
\ dx /

(5/2) / d / d \\
- R exp(I R x) + |--- |--- H(x, t, z)|| exp(I R x)
\ dt \ dt //

2
| (1/2)|
+ exp(-2 Im(R x) + I R x) |H(x, t, z) + R | H(x, t, z)

2
| (1/2)| (1/2)
+ exp(-2 Im(R x) + I R x) |H(x, t, z) + R | R

4
| (1/2)|
- exp(-4 Im(R x) + I R x) |H(x, t, z) + R | H(x, t, z)

/ d \ / d / d \\
+ I |--- H(x, t, z)| + |--- |--- H(x, t, z)||
\ dz / \ dx \ dx //

/ d / d \\\
+ |--- |--- H(x, t, z)||| exp(I R x)
\ dt \ dt ///

2
| (1/2)|
+ exp(-2 Im(R x) + I R x) |H(x, t, z) + R | H(x, t, z)

2
| (1/2)| (1/2)
+ exp(-2 Im(R x) + I R x) |H(x, t, z) + R | R

4
| (1/2)|
- exp(-4 Im(R x) + I R x) |H(x, t, z) + R | H(x, t, z)

4
| (1/2)| (1/2)
- exp(-4 Im(R x) + I R x) |H(x, t, z) + R | R

Error during integration...

Asked by: Don_Caraota 150

February 08 2022

2 5

I was computing an integral (Running Maple 18 on Windows 10):

The classic lenght of arc Integral of sqrt(1+(dy/dx)^2) dx

In this case, the function was a cartesian circle (x-R)^2+y^2=R^2 isolated as y=sqrt(R^2-(x-R)^2)

When I do the integration, the result of the integral is not correct.
But if I change R for a, the result is correct. Why? This does not make any sense.

R wasn't assigned to any variable. The code was:

Good Integral

[>y:=expand(sqrt(a^2-(x-a)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

Wrong Integral

[>y:=expand(sqrt(R^2-(x-R)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

In fact, any UPPERCASE letter used as the radius gives me the wrong answer whereas any LOWERCASE letter gives me the proper result. Why is this?

Thanks and have a nice day
EDIT: I added a Screenshot

How to perform this kind of integrals?...

Asked by: Karch25 40

September 06 2021

2 1

Hello!

I am trying to integrate this function numerically from x=0... 1, by using int and evalf(Int) but maple cannot handle it. Is there another kind of numerical integration?

(2*x-1)^2*(2*n+(5*(2*x-1))*(x-1))*(2*n-5+5*x)*ln(1-(5*(1-x))*x/n)/((1-x)^2*(-2*n-(15*(1-x))*x))

Are there another kind of procedures to do numerical integration?

how can maple be used for Heyting Algebra...

Asked by: kerria 5

August 24 2021

1 0

Bellissima used kripky modules to find the labels for one and two generators. the number of these labels increses to a very large number as we add another level. Can maple help count these lables? and how?