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I was given that solitary initial state to see how it will deform as time goes on. am struggling to get my code so that I can get video frames. please help on how I can generate my code

 

uo(x)= a0x2(1-x)2 for x (less than or equal to) x (less than or equal) 1

u0(x)    = 0 for x > 1

the video clips will be representing the function u(*,t) :x to u(x,t)

for a sequence of choices of t such as t=0; t=0,5...t=3

restart;
Eq1 := diff(T1(t), t) = (W*Cp*(To-T1(t))+UA*(Ts-T1(t)))/(M*Cp);
Eq2 := diff(T2(t), t) = (W*Cp*(T1(t)-T2(t))+UA*(Ts-T2(t)))/(M*Cp);
Eq3 := diff(T3(t), t) = (W*Cp*(T2(t)-T3(t))+UA*(Ts-T3(t)))/(M*Cp);
sys := Eq1, Eq2, Eq3;

Operational Veriables

W := 100;
UA := 10;
Cp := 2;
M := 1000;
To := 20;
Ts := 250;

Initial Conditions

sys1 := {Eq1, Eq2, Eq3};

nsys := nops(sys1);

ics := {T1(0) = 20, T2(0) = 20, T3(0) = 20};
{T1(0) = 20, T2(0) = 20, T3(0) = 20}
nics := nops(ics);
for i from 1 to nics do Sol ||i:=dsolve({sys1, ics[i]},{T1(t),T2(t),T3(t)},numeric)od;
Error, unable to match delimiters
Typesetting:-mambiguous(Typesetting:-mambiguous( for i from 1 to

nics do Sol verbarverbariAssigndsolvelpar(sys1comma ics(i))

commalcubT1(t)commaT2(t)commaT3(t)rcubcommanumericrparod,

Typesetting:-merror("unable to match delimiters")))

 

what is the wrong with Pi set ::: in this function ::: Warning, no iterations performed as initial point satisfies first-order conditions

Optimization[Minimize](x^2 + y^2 + 25*(sin(x)^2+sin(y)^2), x=-2*Pi .. 2*Pi , y= -2*Pi .. 2*Pi);

Warning, no iterations performed as initial point satisfies first-order conditions
[0., [x = HFloat(0.0), y = HFloat(0.0)]]


Optimization[Maximize](x^2 + y^2 + 25*(sin(x)^2+sin(y)^2), x=-2*Pi .. 2*Pi , y= -2*Pi .. 2*Pi);

Warning, no iterations performed as initial point satisfies first-order conditions
[-0., [x = HFloat(0.0), y = HFloat(0.0)]]

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

I got my good result when I apply it with this function :


f:= (x,y)->cos(x)*sin(y) -(x/(y^2+1));


Optimization[Maximize](f(x,y), x = -1 .. 2, y = -1 .. 1);


[0.994945017202501170,[x = HFloat(-0.6362676080636113), y = HFloat(1.0)]]

Optimization[Minimize](f(x,y), x = -1 .. 2, y = -1 .. 1);


[-2.02180678335978703,[x = HFloat(2.0), y = HFloat(0.10578346945175972)]]

i want to find initial condition for F(0),G(0), H(0) and thetap(0) which is are missing in this problem.. then i facing this error Error, (in dsolve/numeric/bvp) Newton iteration is not converging



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/hydronew2.mw .

Download hydronew2.mw

Hi, everyone!

I need help.

There are a system of 2 pde's: 

diff(Y(x, t), x$2) = exp(-2*x*b)*(A(x, t)-Y(x, t)), diff(A(x, t), t) = exp(-2*x*b)*(Y(x, t)-A(x, t)) 

and initial and boundary conditions: 

A(x, 0) = 0, Y(0, t) = 0.1, (D[1](Y))(0, t) = 0. 

Goal: 
For each b = 0, 0.05, 0.1. 
1)to plot 3-d  Y(x,t): 0<=x<=20,0<=t<=7. 
2)to plot  Y(x,4). 

Are there any methods with no finite-difference mesh?


I realized the  methods such as  pds1 := pdsolve(sys, ibc, numeric, time = t, range = 0 .. 7)  can't help me:

Error, (in pdsolve/numeric/match_PDEs_BCs) cannot handle systems with multiple PDE describing the time dependence of the same dependent variable, or having no time dependence 

I found something, that can solve my system analytically: 
pds := pdsolve(sys), where sys - my system without initial and boundary conditions. At the end of the output: huge monster, consisted of symbols and numbers :) And I couldn't affiliate init-bound conditions to it.

I use Maple 13. 

Hello everyone,

I need help to type in the following type of initial condition.

diff(1/x*diff(F(x),x),x)=0 at x =0.

Thanks

In a trivial example of where x goes from 0 to 1 of d n(x)/dx =a, where n(0)=1, n(1)=2, so that the integral is solved easily, how can i do this in maple however I can only solve an eqation with the initial condition, if i try anything else then i get errors such as, 

fx := diff(n(x), x)-a

A := rhs(dsolve({fx, x = 0 .. 1, n(0) = 1, n(1) = 2}, n(x)));

Error, (in dsolve) invalid terms in sum: 0 .. 1

 

 

 

I am trying to get a solution to the heat equation with multiple boundary conditions.

Most of them work but I am having trouble with two things: a Robin boundary condition and initial conditions.

First, here are my equations that work:

returns a solution (actually two including u(x,y,z,t)=0).

 

However, when I try to add:

or

 

I no longer get a solution.

 

Any guidance would be appreciated.

 

Regards.

 

I have uploaded a worksheet with the equations...

Download heat_equation_pde.mw

Hello,

 

I have two sets of data representing two function that depends on x with a parameter A.

I need to do a fit on both data series at the same time so to fit with the best parameter A.

 

Here is how I do a fit on one function

 

> f(x):=A*cos(x-B)^(2);               
> g(x):=A*(cos(x-C)^(2)+ sin(x-C)^(2))^2; 
> fit1 := Fit(f(x), r, x, parameternames = [A, B, C...

Hi I have three differential equations: 

u := diff(P(t), t) = -7*10^(-8)*P(t)*t/(P(t)*t+R(t))^(1/2),

diff(R(t), t) = 7*10^(-8)*t^2*P(t)/(P(t)*t+R(t))^(1/2)+600*(Z(t)^2-10^5*t^3*(1/(1.15*10^12))^(2/3)*e^(-1.15*10^12))/(t*(P(t)*t+R(t))^(1/2)),

diff(Z(t), t) = -4*10^5*(Z(t)^2-10^5*t^3*(1/(1.15*10^12))^(2/3)*e^(-1.15*10^12))/(t^2*(P(t)*t+R(t))^(1/2))

 

and i want to solve them with initial conditions:

initial := R(0) = 0, Z(0) = 0, P(0) = P;

Shifted Data IVP...

December 23 2012 TobiasKr 5

Hello everybody,

I just realised Maple is allowed for my upcoming exam after New Year.

My plan is to have templates of the most common math problems, I might encounter for quick solutions.

Anyway, I have run into a problem with Laplace shifted data, particularly initial value problems. I have been searching for HOURS, and feel like I have look up everything on google, maplesoft and other sites without succes.

I hope some of you are able to help me. The exercise is:

Hello,

I'm trying to solve the effects (deflictions, tensions, etc) of a load on a timoshenko beam. It uses two partial diffential equations, wherein q is the load:

> PDE1 := kappa*G*A*(diff(y(x, t), x, x)-(diff(theta(x, t), x)))-rho*A*(diff(y(x, t), t, t))-q;

> PDE2 := E*J*(diff(theta(x, t), x, x))+kappa*G*A*(diff(y(x, t), x)-theta(x, t))-rho*J*(diff(theta(y, x), t, t));

The boundary conditions are that in the corners the moments (derative of theta...

Hello,

I am trying to add an if statement to maple code for example if U(tk) less or equal to 4 then 
the initial condition=0 else the initial condition=value .
 
I am getting this error:
Error, cannot determine if this expression is true or false: U(365)

restart;

 k := 0; B[1] := 0.001/365; B[2] :=0.002/365:

Hi, i'm trying to solve the following PDE in Maple:

>

Thank you for Assisting me to solve the PDE, Now please would you tell me what F5 means (in other words, explain to me the solution) and also could you how to test if the solution satisfies the initial and boundary conditions.

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