I don't know what is the problem with this. Please take a look at it. Any help is appreciated. Thanks.

Download AA.mw

I want to obtain the taylor series of a function say sin(x) at x=0 up to infinity. I mean that I don't want a trauncated series. I tried using "series" and "taylor" but they just give the truncated series.

Well, long story short. Sat in class, got bored. Began thinking of how to plot different figures in maple.
This eventually leading to that of a rainbow. Anyone got a formula or something i can use to create one? :-)
Thanks ahead. :)

I have the following two PDEs:

PDE := diff(u(x, t), t) = diff(u(x, t), x, x)+sin(x+t)-cos(x+t);

IBC:= D[1](u)(0,t)=-sin(t),
D[1](u)(1,t)=-sin(1+t),
u(x,0)=cos(x);

pds := pdsolve( PDE, [IBC], numeric, time = t, range = 0 .. 1,
spacestep = 1/32, timestep = 1/32,
errorest=true
)

PDE2 := diff(v(x, t), t) = diff(v(x, t), x, x);
IBC2:= D[1](v)(0,t)=0,
D[1](v)(1,t)=-0.000065*v(1, t)^4,
v(x,0)=1;

pds1 := pdsolve( PDE2, [IBC2], numeric, time = t, range = 0 .. 1,
spacestep = 1/32, timestep = 1/32,
errorest=true
);

Now, what I want to do with these two PDEs is the following:

For each h=timestep=spacestep  = 1/16 , 1/32 , 1/64 , 1/128 , 1/256

Calculate the error norm ||E||_h = sqrt(sum_{j=0}^{1/h} h* |u(j*h,tval)-v(j*h,tval)|^2)

where tval is some chosen point between 0 and 1 (this value is fixed for each spacestep chosen).

And then plot the graph of log ||E||_h vs. log h above.

What I don't know is how to extract each time the spacestep and its PDE's two solutions, does someone have a suggested script to use here?

hello guys,

i have a system of autonomous equations which i want to plot its 3D phase space with directional field,

i have some problem with it :dy.mw , and i dont know how to command for add some directional field for 3D phase space .

thank you guys

Dear all;

Good morning everyone.

I solve a simple ode, i want how can I write this program as procedure with output the two coefficient involved in the solution, after solving with ics. i.e coef:=dsolve(ode);  in my example I want as output [4, -1] .

restart:
ode:=diff(y(x),x,x)=3*diff(y(x),x)-2*y(x);
coef:=dsolve(ode);
ics:=y(0)=3, D(y)(0)=2;
dsolve({ics,ode});

with best regards

I do not know! I am a novice in maple as well as in graph theory. I attach a doc in which i attempted to learn what is network. It seems alright with maple as it gives as what it understands as horizontal and vertical network. I do not expect a horizontal line as horizontal network and vertical line as vertical network, in which case a horizontal line with nodes 1 and 2 will be vertical network if  draw it vertically. The maple, in my opinion ( i am not a maple man) gives the answer in a vertical pattern, rightly so for clarity and space constraint.

I am sorry if i am confusing.  The document in my attempt to know more may give you also more insight. Thanks.

Download MyAttempt.mwMyAttempt.mw

Why maple is not plotting the whole surface in the domain specified?

Thanks for the help.

How do I construct the seuqence 1/16 , 1/32 , 1/64 , 1/128 , 1/256 in maple?

What's the syntax?

I looked at the examples in here:

http://www.maplesoft.com/support/help/maple/view.aspx?path=seq

But didn't find something similar.

let γ be the root 

i have to apply taylor series on f(x) and then do some substitution like (helped by a member of Mapleprime)

restart;
taylor(f(x), x = gamma, 8);
f(x[n]) := subs([x-gamma = e[n], f(gamma) = 0, seq(((D@@k)(f))(gamma) = factorial(k)*c[k]*(D(f))(gamma), k = 1 .. 1000)], %)

then find the derivative of result from above output

i do

b := diff((x[n]), e[n])

basically i have to find the value of newton method which is

y_n=x_n-f(x_n)/D(f)(x_n)

here we substitute x_n=γ and D(f)(x_n)=b

and then want to apply f on y_n

there are to problem which i face 

1  f(x_n)/D(f)(x_n) is not in simplified form i-e O(e[n]^8) and O(e[n]^7) is appeared in numerator and denominator respectively. how we get the simplified result.

2 wht step should i do to find f(y_n)

plx help me to do this 

thanx in advance

When I use the option assume = nonnegint or integervariables = {...} in Optimization[Minimize], or Optimization[LPSolve] I've got the message "kernel connection lost'. 

Thie even happens when I use the simple example from the Maple help:

with(Optimization):
LPSolve(2*x+5*y,{3*x-y=1,x-y<=5},assume={nonnegative,integer});

It says; mserver.exe has stopped working. 

What's wrong? 

How can I compute F from G according to the following text? (I implemented this but I need a more efficient implementation.)

Given a set G of polynomials which are a subset of k[U, X] and a monomial order with U << X, we want to comput set F from G s.t.

1. F is subset of G and for any two distinct f1, f2 in F , neither lpp (f1) is a multiple of lpp (f2) nor lpp (f2) is a multiple of lpp (f1).

2. for every polynomial g in G, there is some polynomial f in F such that lpp (g) is a multiple of
lpp (f ), i.e. ⟨lpp (F )⟩ = ⟨lpp (G)⟩,

--------------------------------------------------------------------------------------

It is worth nothing that F is not unique.

Example:  Let us consider G = {ax^2 − y, ay^2 − 1, ax − 1, (a + 1)x − y, (a + 1)y − a} ⊂ Q[a, x, y], with the lexicographic order on terms with a < y < x.

Then F = {ax − 1, (a + 1)y − a} and F ′ = {(a + 1)x − y, (a + 1)y − a} are both considered set.

please not that K[U,X] is a parametric polynomial ring (U is e sequence of parameters and X is a sequence of variables).

lpp(f) is leading monomial of f w.r.t. variables X. For example lpp(a*x^2+b*y)= x^2.

mydoubt-to-mapleprime.mw
an any one help me understand and correct the following errors in maple document. Thanks.

Download mydoubt-to-mapleprime.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

Is there any Maple command for computing the product of two set A and B?

For example if A={a,b,c} and B={x,y} then we have A*B={ax,ay,bx,by,cx,cy}.

Hello,

I have two regimes. Each regime is characterized by system of state differential equations (diff(S(t), t), diff(K(t), t)) and co-state differential equations (diff(psi[S](t), t), diff(psi[Iota](t), t)) as follows: 

(1)

diff(S(t), t) = -eta*K(t)*S(t)/(w*N*(S(t)+K(t))), diff(K(t), t) = eta*K(t)*S(t)/(w*N*(S(t)+K(t)))-upsilon

diff(psi[S](t), t) = eta*K(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2), diff(psi[Iota](t), t) = eta*S(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2)

(2)

diff(S(t), t) = -eta*K(t)*S(t)/(w*N*(S(t)+K(t))), diff(K(t), t) = eta*K(t)*S(t)/(w*N*(S(t)+K(t)))

diff(psi[S](t), t) = eta*K(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2), diff(psi[Iota](t), t) = eta*S(t)^2*(psi[S](t)-psi[Iota](t))/(w*N*(S(t)+K(t))^2)

The first regime is employed from 0 to t1 (where t1 is unknown) and then regime 2, from t1 to T. I know the initial values for the state variables of the first system at t=0, that is, S(0)=S0 and K(0)=K0, as well as boundary conditions for the co-state variables for regime 2 at t=T, that is, psi_S(T)=a and psi_I(T)=b. 

I also know that my unknown t1 should satisfy the algebraic equation: -c - psi_S(t1)=0, where psi_S(t1) is the solution of the co-state diff equation of the regime 2 at t=t1. 

My question is: If I assume that the systems have not analytical solution, how can I found unknown t1 numerically? Moreover, asssume that all other parameters, such as T, eta, upsilon and others are given.