## HELP : got unable to store error...

Hi everyone!

I have a problem solving the nonlinear ode (as attached below). I got this error ---> Error, (in fproc) unable to store '-1.32352941215398+(-0.441176470717993e-1, -0.)' when datatype=float[8]

1) Could someone please explain to me what does the unable store .... error means?

and i will be grateful if you could help me finding the solution out. Thanks in advance

## How do I plot the complex function f(z)=1/(1-z) fo...

How can I plot the complex function f(z)=1/(1-z) for |z|<1 into maple code? (z is a complex number)

Best regards,

Seda

How can I modify the appearance of the arrowheads on the vectors displayed in phaseportrai? In particular, how can I "fill in" the arrowheads so that the arrowhead is not just an outline?

My code is:

phaseportrait([D(x)(t)=-0.4*x(t)+(0.5+4*x(t))*y(t),D(y)(t)=0.4*x(t)-(4.5+4*x(t))*y(t)],[x(t),y(t)],t=0..100,[[x(0)=1,y(0)=0.0]],x=0..1,y=0..0.1,stepsize=0.01,scaling=UNCONSTRAINED,linecolour=BLACK,dirgrid=[17,17],linestyle=1,arrows=SLIM,axes=BOXED);

Thank you

## How to solve BVP by shooting method?...

Hi everyone,

I'm kinda new here, and I really hope you guys can help me through this. In my new case study, after some revision, i thought i might be trying to implement a shooting method. I tried my best to make it work/understand but i couldn't get to any result.

So, as attached (i re-do PV Satya Naraya's paper first to be more understand but .....)

Here is my questions and the worksheet:

1) really stuck in mind - what is the purpose of shooting method for some related study?

2) what is the meaning of error .............'use midpoint method intead"

3) Worksheet - 1MASS_JEFF_SATYA_on_Beta.mw

Thanks in advanced. Really hope that someone can help/teach me how to solve the boundary value problem by shooting method.

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## How to draw these geometric objects?...

Hi, there

How can I draw the excircles, incircles,circumcircle and their centers of a triangle simultaneously with maple13 in a geometric plot? please specify the commands.

M.R.Yegan

## Possible bug in Eingenvalues...

I am using maple 13 to found Eingenvalues of an hermitian matrix :

M1:=Matrix([
> [lambda3+lambda4,0,0,0,0,0,lambda4/sqrt(2),0,0,I*lambda4/sqrt(2)],
> [0,lambda3/4,0,0,0,0,0,0,0,0],
> [0,0,lambda3/4,0,0,0,0,0,0,0],
> [0,0,0,lambda3/4,0,0,0,0,0,0],
> [0,0,0,0,lambda3/4,0,0,0,0,0],
> [0,0,0,0,0,lambda3,0,0,0,0],
> [lambda4/sqrt(2),0,0,0,0,0,lambda3/2,0,0,0],
> [0,0,0,0,0,0,0,lambda2,0,0],
> [0,0,0,0,0,0,0,0,lambda2,0],
> [-I*lambda4/sqrt(2),0,0,0,0,0,0,0,0,lambda4/2]
> ]);

>Eigenvalues(M1);

my surprise is that maple gives me 8 correct solutions an 2 complex eigenvalues which are not acceptable (we now that the eigenvalues for an hermitian matrix are all real) .

To understand the output of maple, first,  I suspect that the complex part of the roots was null but without success I haven't found how to do it zero...

is it a bug? Thanks a lot to cooperation

## 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?

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

## Two plots together...

Hi Maple People,

My question is, "How can I combine the two plots shown in the attachment into one plot?".

Regards

Matt

## Differential equation in Maple...

Hello

I am new to Maple. I am solving the differential equation with the given initial condition. I am getting some error. Can anyone help me please.

Thanks

maple_help.mw

## 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

## Equations of motions for Euclidean and Minkowski...

by: Maple 13

This procedure calculate the equations of motions for Euclidean space and Minkowski space  with help of the Jacobian matrix.

Procedures
Calculation the equation of motions for Euclidean space and Minkowski space

 Calling Sequence

Parameters

 parameterSequence - eq out equation of motion g out metric xup out velocitiy vector xa in position vector xu in vector of the independet coortinates eta in signature matrix for Minkowski space var in independet variable

 >

Procedur Code

 >
 >

Input

 >

 >

Output EOM

 >
 (5.1)

Output Line-Element

 >
 (6.1)

Output Metric

 >
 (7.1)
 >
 >

Procedures
Calculation the equation of motions for Euclidean space and Minkowski space

 Calling Sequence

Parameters

 parameterSequence - eq out equation of motion g out metric xup out velocitiy vector xa in position vector xu in vector of the independet coortinates eta in signature matrix for Minkowski space var in independet variable

 >

Procedur Code

 >
 >

Input

 >

 >

Output EOM

 >
 (5.1)

Output Line-Element

 >
 (6.1)

Output Metric

 >
 (7.1)
 >
 >

## Einstein Field Equations...

I am using maple 13 to get the result of the einstein field equations,

with(tensor)

...

Estn := Einstein(metric, RICCI, RS);

displayGR(Einstein, Estn);

How can I put the result on an array element, so I can use it later on?

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