I'm trying to build a Maple procedure that will generate vector fields on a metric with certain properties. Working with metric g over the coordinates {u,v,w}, call the field X = (a(u,v,w), b(u,v,w), c(u,v,w)). The field should satisfy <X, X> = 0 and have the directional covariant derivative of X in the direction of each coordinate vector field = 0 (with resepct to the Levi-Civita conenction).

Basically, these conditions yield a system of 3 PDEs and an algebraic expressionin terms of a,b,c. I've been trying to solve them using pdsolve, but I'm getting the error message:

>Error, (in pdsolve/sys) the input system cannot contain equations in the arbitrary parameters alone; found equation depending only on _F1(u,v,w): _F1(u,v,w)

I've attached my worksheet. Can anyone help me out?

Thanks! ppwaves.mw

Hello,

i am trying to get a latex output which equals the displayed maple equations, where i am using alias/surpress or declare to shorten the dependencies of my derivatives. Whereas in Maple this looks how i want it to look like, i can not get the latex() command to apply the aliases. Instead it replaces the short forms with the long terms before creating the latex code. Is there anyway to get a latex output directly from the displayed math WITH alias?

2 small examples:

Both yield  $ X \left( a,b,c \right)$ whereas i would like to get X. Simply substituing changes the partial differential symbol to "d" in the latex output and makes the equations unuseable, so this is no option i guess..

Thanks a lot for any suggestions!

I have the following integral equation to solve numerically:

v(x,t)=1 - h*\int_0^t JacobiTheta0(1/2x , \pi i s) v^4(1,t-s)ds

where h is a numerical parameter, and v(1,t) = 1-h*\int_0^t \theta_3(r)v^4(1,t-r)dr (theta3 is Jacobi theta3 function).

So I want to use an iteration method that will converge numerically to the solution, where v(1,0)=1.

How to use maple for this?

I want also to find the rate of convergence to the numerical solution.

 edit: I should note that v(x,0)=1, even though it's implied from v(x,t) above.

I have three cylinders as follows.

with(plots);
with(plottools);
p1 := cylinder([1, 1, 1], 1, 1);
p2 := cylinder([1, 1, 1], 2, 3);
p3 := cylinder([1, 1, 1], 1, 4);

I want to display in order where p1 is at the bottom, then p2, and then p3 on the top of p2. Thank you for your assistance.

I have the following PDE system to solve numerically and I am not sure how to use maple to solve it.

v_t = v_{xx} for 0<x<1 , t>0

v(x,0)=1

v_x(1,t)=-hv^4(1,t) (where h is some numerical number);

v_x(0,t)=0

To solve this pde numerically I need to use the following condition on v(1,t):

v(1,t) = 1-h*\int_{0}^t \theta_3(\tau)v(1,t-\tau)^4d\tau

this is the numerical boundary condition, where \theta_3 is Jacobi theta3 function.

I don't see how can I use maple for this numerical pde problem.

Here's my attempt at solution:

[code]

 PDE := diff(v(x, t), t) = diff(v(x, t), x, x);

JACOBIINTEGRAL := int(JacobiTheta3(0, exp(-Pi^2*s))*v(1, t-s)^4, s = 0 .. t);

IBC := {`&PartialD;`(v(0, t))/`&PartialD;`(x) = 0, `&PartialD;`(v(1, t))/`&PartialD;`(x) = -0.65e-4*v(1, t)^4, v(x, 0) = 1};

pds := pdsolve(PDE, IBC, numeric, time = t, range = 0 .. 1, spacestep = 0.1e-2, timestep = 0.1e-2, numericalbcs = {v(1, t) = 1-0.65e-4*JACOBIINTEGRAL}, method = ForwardTimeCenteredSpace)

[/code]

But I get the next error message:

Error, (in pdsolve/numeric/process_IBCs) improper op or subscript selector

How to fix this or suggest me a better way to solve this pde numerically?

multiple_parameters_-_sipa.mw 

@Carl Love please help me .. I tried solve a ode system of equation problem numerically with your code, using maple 15 but i get errors.

I dont know how to plot multiple solutions on one graph.

I want to vary one of the parameters....

e.g s1=0, s1=0.5, s1=1 where other parameters are kept constant

> restart;
> g := 1/7; alpha1 := .75; alpha2 = .5; `&alpha;v` := .3; xi := .4; `&mu;v` := 1/30; mu1 := 0.434931506849e-4; mu2 := 0.410958904109e-4; `&mu;h` := 1/(60*365); Nh := 10000; a := 1; Nv := 1000; s2 := .5; br := 4;
> A1 := diff(S0(t), t) = (1-s1)*mu1*Nh+(1-s2)*mu2*a-br*alpha1*S0(t)*V1(t)/Nh-`&mu;h`*S0(t);
> A2 := diff(Z0(t), t) = xi*Z(t)-br*alpha2*Z0(t)*V1(t)/Nh-`&mu;h`*Z0(t);
> A3 := diff(Iota(t), t) = br*alpha1*S0(t)*V1(t)/Nh-g*Iota(t)-`&mu;h`*Iota(t);
> A4 := diff(Y(t), t) = br*alpha2*Z0(t)*V1(t)/Nh-g*Y(t)-`&mu;h`*Y(t);
> A5 := diff(Z(t), t) = s1*mu1*Nh+s2*mu2*a+g*(Iota(t)+Y(t))-xi*Z(t)-`&mu;h`*Z(t);
> A6 := diff(V0(t), t) = `&mu;v`*Nv-br*`&alpha;v`*V0(t)*Iota(t)/Nh-`&mu;v`*V0(t);
> A7 := diff(V1(t), t) = br*`&alpha;v`*V0(t)*Iota(t)/Nh-`&mu;v`*V1(t);

> PD := unapply({A || (1 .. 7)}, s1);
> IBC := {S0(0) = 450, V0(0) = 100, V1(0) = 70, Y(0) = 50, Z(0) = 250, Z0(0) = 50, Iota(0) = 100};
> sList := [0, .6, 1]; Colours := table(`~`[`=`](sList, ["blue", "red", "green"])); for s1 in sList do pds := dsolve(PD(s1), IBC, numeric); Plots[s1] := pds:-plot[display](Iota(t), t = .5, linestyle = "solid", colour = Colours[s1], legend = sprintf("s1=%2.2f", s1), title = "Velocity Profile") end do;
Error, (in dsolve/numeric/process_input) invalid argument: {S0(0) = 450, V0(0) = 100, V1(0) = 70, Y(0) = 50, Z(0) = 250, Z0(0) = 50, Iota(0) = 100}

> plots:-display([seq(Plots[s1], `in`(s1, sList))]);
Error, (in plots:-display) expecting plot structures but received: [Plots[0], Plots[.6], Plots[1]]

Download multiple_parameters_-_sipa.mw

Hi EveryOne!

Let matrix M over GF(2ⁿ)/f(x). How to compute:

1. Rank of M.

2. Sum of the elements and Square of this Sum in any row of M (i.e: Sum=m_i0 + m_i1 + ... + m_in, and Sum² ).

3. New matrix M, where in row i  m_i0 = m_i0/Sum², m_i1 = m_i1/Sum², ..., m_in = m_in/Sum².

Please help me. Thank you very much.

Given a polynomial in several variables is it possible to split it so that all the coefficients of the monomials are +1 or -1.

Example:

p:=-z+2*x+4*y-3*x*y.

I would lie to obtain

f:=-z +x+x +y+y+y+y -x*y-x*y-x*y.

Given a polynomial expression I would like to obtain a list whose entries are the positive entries of the polynomial with multiplicity given by the coefficients:

Example:

Given the polynomial expression: p:=x^2*y-2*y*z+3*x^2+2*y-z

The positive terms are: x^2*y, 3*x^2, 2*y

Thus I would like to obtain the list L:=[x^2*y , x^2 , x^2 , x^2, y , y].

Notice x^2*y appears once since the coefficient is 1.

x^2 appears three times since the coefficient is 3.

y appears two times since the coefficient is 2.

Is there a way to divide two lists entry by entry. I mean the following:

L:=[2,4,6,3];

T:=[2,2,3,1];

L/T=[1,2,2,3]

Given a list of numbers, is there a command that returns the list whose entries are the absolute values of the original list? is there also one from the signum?

Ex: Given L:=[1,-1,-5,2,-3], I would like to obtain for the absolute value [1,1,5,2,3] and for the signum [1,-1,-1,1,-1].

Given a list I would like to find the position of the positive numbers. Ex: Given L:=[3,8,-5,1,-3,-7], I would like to have as a result P:=[1,2,4].

I want to avoid using a loop for this. Any suggestion?

I can read a .m file written using "save" command, However the variable list (pallete) doesn't get updated. Is there any way to see the list of variables and their values that has been read with "read" command from the .m file?

Hello,

I need to solve the next ode:

diff(u(x, y), x) = -(2/3)*(3*h^3*nu+9*h^2*nu*y-12*nu*y^3+36*x^2*y+56*y^3)/h^3

diff(v(x, y), y) = (2/3)*(36*nu*x^2*y+56*nu*y^3+3*h^3+9*h^2*y-12*y^3)/h^3

diff(u(x, y), y)+diff(v(x, y), x) = -(6*(1+nu))*x*(h^2-4*y^2)/h^3

The inicial conditions are:

u(L, 0) = 0
v(L, 0) = 0
D[1]*u(L, 0) = 0

When I write on Maple this code, he give me a error:

with(PDEtools, casesplit, declare); declare((u, v)(x, y))

sys2 := [diff(u(x, y), x) = -(2/3)*(3*h^3*nu+9*h^2*nu*y-12*nu*y^3+36*x^2*y+56*y^3)/h^3, diff(v(x, y), y) = (2/3)*(36*nu*x^2*y+56*nu*y^3+3*h^3+9*h^2*y-12*y^3)/h^3, diff(u(x, y), y)+diff(v(x, y), x) = -(6*(1+nu))*x*(h^2-4*y^2)/h^3]

sol := pdsolve(sys2)

ics := u(L, 0) = 0, v(L, 0) = 0, D[1]*u(L, 0) = 0

pdsolve([sys2, ics]);

Why Maple can't solve this PDE?

I think that the problem is on sys2. But I don't know how to explain to Maple the function: diff(u(x, y), y)+diff(v(x, y), x) = -(6*(1+nu))*x*(h^2-4*y^2)/h^3; on the system of equations. I think the problem is there.

I'm so sorry by my bad english.

I need to solve this, anyone help me please.

Thanks.

Please I need some assistance on how to solve the below pde:

diff(c(x,t),t)=diff(c(x,t),x,x)-diff(c(x,t),x)-c(x,t)

I have my initial condition and 2 boundary conditions. I just need some clues on how to go about solving the problem. Thank you!