## Maple Code to solve Perturbation Iteration Solutio...

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....

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+a1ν1/j+...+anνn/j

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

k1+(a1+...)ν1/j+...+(ak+...)ν(j-1)/j

where ki, ai 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...

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...

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...

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...

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 := psi*S(t) -(delta + mu)*E(t);
 (2)
 > f__3 := Delta*E(t) -(gamma+gamma__1 + mu)*X(t);
 (3)
 > f__4 := gamma__1*X(t)-(eta + xi + mu)*H(t);
 (4)
 > f__5 := xi*H(t) - mu*R(t);
 (5)
 > f__6 := gamma*X(t)-eta*H(t) - d*D(t);
 (6)
 > f__7 := b*D(t) - b*B(t);
 (7)
 > f__8 := phi__p + sigma*X(t)+eta__1*H(t) +d__1*D(t)+ b__1*B(t) - alpha*P(t);
 (8)

## PDETools:-pdsolve other solutions...

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...

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...

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)

4
|              (1/2)|   (1/2)
- exp(-4 Im(R x) + I R x) |H(x, t, z) + R     |  R
collect(%, exp(I*R*x));
/  (5/2)       / d            \      2
|-R      + 2 I |--- H(x, t, z)| R - R  H(x, t, z)
\              \ dx           /

/ 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...

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

## How to perform this kind of integrals?...

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...

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?

## How to solve this PDE equation...

Dear maple users

Greetings.

I hope you are all fine.

In this code, I am solving the PDEs via pdsolve with numeric.

There is some mistake in the boundary condition and pdsolve.

Kindly help me that to get the solution for this PDE.

In this problem h(z) is piecewise

Bc:

code:JVB.mw

Note: z=0.5: