## how can i use do loop in maple?...

if i m working in maple 13 i have to solve a non linear integral equation then what will be the steps to use the do loop.

## scheme of fractional differential equation in mapl...

i want a scheme of fractional differential equation so that i solve my questions and make a code of it.

please provide me the scheme

## Problem in dsolve ...

Dear Maple researchers

I have a problem in solving a system of odes that resulted from discretizing, in space variable, method of lines (MOL).

The basic idea of this code is constructed from the following paper:

http://www.sciencedirect.com/science/article/pii/S0096300313008060

If kindly is possible, please tell me whas the solution of this problem.

With kin dregards,

Emran Tohidi.

My codes is here:

> restart;
> with(orthopoly);
print(`output redirected...`); # input placeholder
> N := 4; Digits := 20;
print(`output redirected...`); # input placeholder

> A := -1; B := 1; rho := 3/4;
> g1 := proc (t) options operator, arrow; 1/2+(1/2)*tanh((1/2)*(A-(2*rho-1)*t/sqrt(2))/sqrt(2)) end proc; g2 := proc (t) options operator, arrow; 1/2+(1/2)*tanh((1/2)*(B-(2*rho-1)*t/sqrt(2))/sqrt(2)) end proc;
print(`output redirected...`); # input placeholder
> f := proc (x) options operator, arrow; 1/2+(1/2)*tanh((1/2)*x/sqrt(2)) end proc;
print(`output redirected...`); # input placeholder
> uexact := proc (x, t) options operator, arrow; 1/2+(1/2)*tanh((1/2)*(x-(2*rho-1)*t/sqrt(2))/sqrt(2)) end proc;
print(`output redirected...`); # input placeholder
> basiceq := simplify(diff(uexact(x, t), `\$`(t, 1))-(diff(uexact(x, t), `\$`(x, 2)))+uexact(x, t)*(1-uexact(x, t))*(rho-uexact(x, t)));
print(`output redirected...`); # input placeholder
0
> alpha := 0; beta := 0; pol := P(N-1, alpha+1, beta+1, x); pol := unapply(pol, x); dpol := simplify(diff(pol(x), x)); dpol := unapply(dpol, x);
print(`output redirected...`); # input placeholder
> nodes := fsolve(P(N-1, alpha+1, beta+1, x));
%;
> xx[0] := -1;
> for i to N-1 do xx[i] := nodes[i] end do;
print(`output redirected...`); # input placeholder
> xx[N] := 1;
> for k from 0 to N do h[k] := 2^(alpha+beta+1)*GAMMA(k+alpha+1)*GAMMA(k+beta+1)/((2*k+alpha+beta+1)*GAMMA(k+1)*GAMMA(k+alpha+beta+1)) end do;
print(`output redirected...`); # input placeholder
> w[0] := 2^(alpha+beta+1)*(beta+1)*GAMMA(beta+1)^2*GAMMA(N)*GAMMA(N+alpha+1)/(GAMMA(N+beta+1)*GAMMA(N+alpha+beta+2));
print(`output redirected...`); # input placeholder
> for jj to N-1 do w[jj] := 2^(alpha+beta+3)*GAMMA(N+alpha+1)*GAMMA(N+beta+1)/((1-xx[jj]^2)^2*dpol(xx[jj])^2*factorial(N-1)*GAMMA(N+alpha+beta+2)) end do;
print(`output redirected...`); # input placeholder
> w[N] := 2^(alpha+beta+1)*(alpha+1)*GAMMA(alpha+1)^2*GAMMA(N)*GAMMA(N+beta+1)/(GAMMA(N+alpha+1)*GAMMA(N+alpha+beta+2));
print(`output redirected...`); # input placeholder
> for j from 0 to N do dpoly1[j] := simplify(diff(P(j, alpha, beta, x), `\$`(x, 1))); dpoly1[j] := unapply(dpoly1[j], x); dpoly2[j] := simplify(diff(P(j, alpha, beta, x), `\$`(x, 2))); dpoly2[j] := unapply(dpoly2[j], x) end do;
print(`output redirected...`); # input placeholder
print(??); # input placeholder
> for n to N-1 do for i from 0 to N do BB[n, i] := sum(P(jjj, alpha, beta, xx[jjj])*dpoly2[jjj](xx[n])*w[i]/h[jjj], jjj = 0 .. N) end do end do;
> for n to N-1 do d[n] := BB[n, 0]*g1(t)+BB[n, N]*g2(t); d[n] := unapply(d[n], t) end do;
print(`output redirected...`); # input placeholder
> for nn to N-1 do F[nn] := simplify(sum(BB[nn, ii]*u[ii](t), ii = 1 .. N-1)+u[nn](t)*(1-u[nn](t))*(rho-u[nn](t))+d[nn](t)); F[nn] := unapply(F[nn], t) end do;
print(`output redirected...`); # input placeholder
> sys1 := [seq(d*u[q](t)/dt = F[q](t), q = 1 .. N-1)];
print(`output redirected...`); # input placeholder
[d u[1](t)
[--------- = 40.708333333333333334 u[1](t) + 52.190476190476190476 u[2](t)
[   dt

2          3
+ 39.958333333333333334 u[3](t) - 1.7500000000000000000 u[1](t)  + u[1](t)

+ 7.3392857142857142858

- 3.6696428571428571429 tanh(0.35355339059327376220

+ 0.12500000000000000000 t) - 3.6696428571428571429 tanh(
d u[2](t)
-0.35355339059327376220 + 0.12500000000000000000 t), --------- =
dt
-20.416666666666666667 u[1](t) - 25.916666666666666667 u[2](t)

2          3
- 20.416666666666666667 u[3](t) - 1.7500000000000000000 u[2](t)  + u[2](t)

- 3.7500000000000000000

+ 1.8750000000000000000 tanh(0.35355339059327376220

+ 0.12500000000000000000 t) + 1.8750000000000000000 tanh(
d u[3](t)
-0.35355339059327376220 + 0.12500000000000000000 t), --------- = 29.458333333\
dt

333333333 u[1](t) + 38.476190476190476190 u[2](t)

2          3
+ 30.208333333333333333 u[3](t) - 1.7500000000000000000 u[3](t)  + u[3](t)

+ 5.4107142857142857144

- 2.7053571428571428572 tanh(0.35355339059327376220

+ 0.12500000000000000000 t) - 2.7053571428571428572 tanh(
]
-0.35355339059327376220 + 0.12500000000000000000 t)]
]
> ics := seq(u[qq](0) = evalf(f(xx[qq])), qq = 1 .. N-1);
print(`output redirected...`); # input placeholder
u[1](0) = 0.38629570659055483825, u[2](0) = 0.50000000000000000000,

u[3](0) = 0.61370429340944516175
> dsolve([sys1, ics], numeic);
%;
Error, (in dsolve) invalid input: `PDEtools/sdsolve` expects its 1st argument, SYS, to be of type {set({`<>`, `=`, algebraic}), list({`<>`, `=`, algebraic})}, but received [[d*u[1](t)/dt = (20354166666666666667/500000000000000000)*u[1](t)+(13047619047619047619/250000000000000000)*u[2](t)+(19979166666666666667/500000000000000000)*u[3](t)-(7/4)*u[1](t)^2+u[1](t)^3+36696428571428571429/5000000000000000000-(36696428571428571429/10000000000000000000)*tanh(1767766952966368811/5000000000000000000+(1/8)*t)-(36696428571428571429/10000000000000000000)*tanh(-1767766952966368811/5000000000000000000+(1/8)*t), d*u[2](t)/dt = -(20416666666666666667/1000000...

## Simulation in celestial mechanics...

How difficult is it to simulate gravitational influences and perturbing effects on celestial orbits with Maple? Could this syntax http://www.maplesoft.com/applications/view.aspx?SID=4484&view=html be altered without excessive changes to consider these aspects?

Are there somewhere worksheets to take a look at as an introduction and to see how such goals would be approached and implemented?

## Adding astronomical coordinates ...

Some time ago, I have used the Virtual 3D Solar System code to plot a few interesting figures with asteroids. It can be found here: http://www.maplesoft.com/applications/view.aspx?SID=4484&view=html . I plotted the asteroid belt as a closed, warped surface according to how the asteroids are inclined, with the arguments of perihelion and longitude of ascending node where they cross the equatorial plane to the other celestial hemisphere. The plot was only done with axes in units of distances, for convenience's sake in astronomical units of 1 AU = 150 million km.

But I am strongly wondering if it were somehow possible to alter or adjust the code such that there is a zylinder placed around such plot where one can see celestial coordinates (Rectascension, Declination) on the inside, so that if one wants to know what coordinates an orbit of a specific asteroid has that one can look in the chart and go out on the balcony and set the telescope to these coordinates. Of course the asteroid most likely is not there on his entire orbital path, but you have at least the location where the asteroid CAN be. Would this be possible to plot?

This probably doesn't work if a closed cylinder is placed around the Virtual Solar System. But how about scrolling the cylinder and the orbits flat on a 2D plot?

I need to calculate Weyl scalar for a metric using null tetrad using debever package in maple 13. However, I am stuck at the defination of h (representing the covariant complex null tetrad). Is it the product of covariant null tetrad? I have worked it out by using covariant, contravariant and both covariant and contravariant null tetrad (like l_a*l_a, l^a*l^a, l_a*l^a), however, i am not getting the right result not even for the example given in the maple help for plane wave. please help me out that how should i define this h.

thanks,
suresh

## The color option of plot...

Hi Maple People

# Some Maple code
restart
x:= Vector(10):
y:= Vector(10):

for z from -5 to 4 do
x[z+6]:=z^2 + 40:
y[z+6]:=z^2 + z + 41:
end do:

plot(x,y,style=point,symbol=asterisk)

Regards

Matt

## How to convert expression to sum?...

I get the maple result as a product and sum off terms

x= (a+b*c)/d

i want to convert it to

x= a/d+b*c/d

i try to use convert(x,?)

## How to optimize this code?...

a1:= f(x) :
> T1 :=simplify((taylor(a1,x=alpha,N+3))):
> E1:=subs([seq(((D@@i)(f))(alpha) = 0,i=1..m-1),f(alpha)=0,x=e[n]+alpha],T1):
> g1 :=(convert(simplify(series((E1,e[n]=0,N))),polynom));

## How to express this constraint into Maple?...

Hi everyone...!

Can somebody tell me how to express this equation in Maple?

xij <= zkl ; ∀ i ∈ I: S(i)=k, ∀ j ∈ B: R(j)=l;

Currently I'm dealing with containerization problem and have 4 indexes in the constraints (namely: i for item, j for container, k for shipment, l for route, S for Set of Shipment, and R for Set of Route) while x and z are binary variables. What I want to express is: (for example), item 1,2,3 are in shipment 1, item 4,5 are in shipment 2, etc etc. SO, if i = 1,2,3 then the value of k will be 1. If i = 4,5 then the value of k will be 2, etc. Same thing goes to j and l, (for example) if j = 1,2 then the value of l will be 1, etc etc. Further depcition is more or less like this:

S(i) = k

S(1) = 1

S(2) = 1

S(3) = 1

S(4) = 2

S(5) = 2

Thank you very much for the help.

## Two independent variables...

HI, I am trying to solve two PDEs but in boundry conditions there is arising an error plz help.
Nazi.mw

## lambda for higher order ODE...

hi, I want calculate lambda(lagrange multiplier) for lane emden type equation, I have made a programme for it but here is error at the end of programme,plz help

lambda.3rd.mw

## How to solve those ODEs ?...

plz help me, how do i solve singular ODEs of lane Emden type equation for homotopy analysis method in maple? there is arising an arror, invalid fraction

## DELAY DIFFERENTIAL EQN 2...

please write a program on matlab or maple for this dde

y'(x)=-y(x-pi/2)       0<x<=10

y(x)=sin(x)       x<=0

tau=pi/2

IT IS URGENT PLEASE

## Length of output exceed limit 1000000...

can anybody help me? i want to check the consistency of my scheme. My equation is too long if i check manually, so i used maple 13 to simplify my equation. But it cannot simplify it because of length of output exceed limit 1000000

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