HI.

I need your remarks in this problem.

I have ode. diff(y(x),x)=f(x,y);  x in [0,a]; h:=a/(2*N); stepsize.

When the the true solution is not Known, we can test the rate of convergence, of numerical solution. The Numerical solution generated when the stepsize is 2*h denoted by y_i^(2h) and the numerical solution with step size h will be denoted by y_i^(h).

if we define the epsilon(h):=sqrt (  1/(N+1)*add(  (y_i^(2h) -y_(2i)^(h) )^2, i=0..N));

 If we useForward Euler ( it's Known that the golbal error isof order 1 and local error of order 2) in the case when the exact solution is know.

But, If we use epsilon(h), and for the same method can some one know the order of Error =h^?????.

Thank you.

restart;
g:=0.88641:
e:=2.53128:
eq:=tan(g)= e*sin(f)/(1+e*cos(f)):
fsolve(eq,f);

gives  1.19749

What command/option do I need to get both solutions like with Mathematica:

g = 0.886461;
e = 2.53128;
eq = Tan[g] == (e Sin[f])/(1 + e Cos[f]);
NSolve[eq, f]

  (*   {{f -> -2.56623}, {f -> 1.19756}} *)

thanks

I took a calculus 1 class in 2002, so i have many maple worksheets i would like to view on my new dell venue 8 pro. can the player read the .mws ext ?  Donald Altringer

ps. I have maple 8 on my laptop but not on th tablet and i don't  have a way of installing it

Hi!

I have the following function:

and I want to calculate it for a certain set of r, theta and t, but when I use subs, the theta variable is also subsituted int the integral's parameters and I get the folllowing result:

I really don't understand why it does that given that there is no issue for the r variable...

Thanks in advance for your help!

P-S: please forgive my poor English : I'm a French student...

Florent

Dear all

Please I need your help to simplify by the coefficient a in this Matrix

I have The matrix A defined by  A:=Matrix(2,2, [[a,a],[3*a,4*a]]);

I want with maple transform A to  A:=a*Matrix(2,2, [[1,1],[3,4]]);

Thanks for your Help.

I try to solve these two nonlinear odes, but no desire outcome. Please helpreal_work1.mwreal_work1.mw  or real_work1.mw

Dear all,

Thanks for your answer. I have a simple question:

Let A be a Matrix, X[1] and X[2] two vectors.

I have this equation:  X[2]= X[1]+ A*X[1]+A*X[2];  Using Maple how can I  writte X[2] =P*X[1]; where P is a matrix to be founded.

Here, P:=(Id-A)^(-1)*A; But how using maple.

I have tried to use Maple to solve ordinary differential equations but i have this error. Could you please help me to fix this problem

> eq1 := diff(v1(t), t) = v2(t);
> eq2 := diff(v2(t), t) = -v1(t)+(3*(v1(t)^2-1))*v2(t);
> init1 := v1(0) = 2;
> init2 := v2(0) = 0;
> with(DEtools);
> DEplot({eq1, eq2}, [v1(t), v2(t)], 0 .. 3*Pi, {[0, 0, 0]}, scene = [v1, v2], stepsize = .1);

Error, (in DEtools/DEplot/direction) division by zero

thank you

b := 1;

h := 1;

A := b*h;

E := 210*10^9;

qr := 100;

Dp := (1/12)*E*b*h^3;

R := 20;

teta := 3;

sys1 := {(E.A+Dp/R^2)*(diff(u(t), `$`(t, 2))) = -E*A*(diff(w(t), t))/R+Dp*(diff(w(t), `$`(t, 3)))/R, -Dp*(diff(w(t), `$`(t, 4))) = E*A*(diff(u(t), t))/R-Dp*(diff(u(t), `$`(t, 3)))/R+E*A/R-100};

dsolve(sys1);

#THİS GAVE ME THE RESULTS LİKE THAT:

{u(t) = (1/4801)*_C3*(-1+sqrt(4801))^(3/2)*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801)*_C4*(-1+sqrt(4801))^(3/2)*exp((1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801*I)*_C5*(1+sqrt(4801))^(3/2)*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)-(1/4801)*_C6*(-1+sqrt(4801))^(3/2)*exp((1/20)*sqrt(-1+sqrt(4801))*t)+(1/4801)*_C3*sqrt(-1+sqrt(4801))*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)-(1/4801)*_C4*sqrt(-1+sqrt(4801))*exp((1/20)*sqrt(-1+sqrt(4801))*t)+(1/4801*I)*_C5*sqrt(1+sqrt(4801))*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)-(1/4801)*_C6*sqrt(-1+sqrt(4801))*exp((1/20)*sqrt(-1+sqrt(4801))*t)-(104999999/105000000)*t+_C1, w(t) = _C2+_C3*exp(-(1/20)*sqrt(-1+sqrt(4801))*t)+_C4*exp((1/20)*sqrt(-1+sqrt(4801))*t)+_C5*exp(-(1/20*I)*sqrt(1+sqrt(4801))*t)+_C6*exp((1/20)*sqrt(-1+sqrt(4801))*t)}

#SO THERE ARE 6 UNKOWN(C1...C6) SO I NEED 6 CONDITION. MY BOUNDRY CONDITIONS:

bs := u(0) = 0, (D(u))(0) = 0, w(0) = 0, (D(w))(0) = 0, w(teta) = 0, (D(w))(teta) = 0;

> r := dsolve({bs, sys1});
%;
Error, (in dsolve) invalid arguments; expected an equation, or a set or list of them, received: {{-17500000000*(diff(diff(diff(diff(w(t), t), t), t), t)) = 10500000000*(diff(u(t), t))-875000000*(diff(diff(diff(u(t), t), t), t))+10499999900, 210043750000*(diff(diff(u(t), t), t)) = -10500000000*(diff(w(t), t))+875000000*(diff(diff(diff(w(t), t), t), t))}}
>

I tried to change the equations row. But ı dont understand where something wrong.I tried so many times. May u please find where ıt is wrong? 

Hello,

I would like to know whether it is possible to change the color of animations that have already been produced and assigned to a variable.

Let's take for example

P := plots:-animate(plot, [sin(x+t), x = -Pi .. Pi], t = -Pi .. Pi, frames = 8)

is there a command to change the color of the curve AFTER it has been produced?

The calculus to generate all my plots took 4 hours so I would like not to have them calculated again.

Thx

How can I typeset this in Maple? A ket with a 2 element column vector in it, but without the vector brakets. Like this:

| x over y >

Thanks

AOA... Pl correct it

Help.mw

can we load part of a package not the package whole !? for example from physics package i only need diff tool not all of the package tools,can i do sth for that !? 

restart:

Eq1:=diff(psi(y),y$4)-diff(psi(y),y$2)=0;

dsolve({Eq1});

bcs:=psi(h1)=F,D(psi)(h1)=-1,psi(h2)=-F,D(psi)(h2)=-1;

dsolve({Eq1,bcs});

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: [{psi(h1), psi(h2), psi(y)}, {psi(h2), psi(y)}]

Any suggestion?

Cheers!

Dear all;

Please see only the last lines of this procedure,

1)I ask if this procedure give an output epsilon(x0,h). Really, I need your help. Thanks.

2) Can we plot epsilon(x0,h), versus h

> heun := proc (x0, h)

local x, y, i, N, k, f, ode, k1, k2, x1, x2, y1, y2;

f :=(x,y)-> 1/(1+cos(y)) ;

ode := diff(y(x), x) = f(x, y);

N := round((1/2)*x0/h);

y2 := Array(0 .. N);

x2 := Array(0 .. N);

y1 := Array(0 .. 2*N);

x1 := Array(0 .. 2*N);

x2[0] := 0; y2[0] := (1/4)*Pi;

for i from 0 to N-1 do

x1[2*i+2] := (2*i+2)*h;  k1[1] := f(x1[2*i], y1[2*i]); 

k1[2] := f(x1[2*i]+h, y1[2*i]+h*k1[1]);

y1[2*i+2] := y1[2*i]+(1/2)*h*(k1[1]+k1[2]);

x2[i+1] := (2*i+2)*h;

k2[1] := f(x2[i], y2[i]);

k2[2] := f(x2[i]+2*h, y2[i]+2*h*k2[1]);

y2[i+1] := y2[i]+h*(k2[1]+k2[2])

end do;

return firstresulat = evalf([seq([x2[i], y2[i]], i = 0 .. N)]);

return secondresulat =evalf([seq([x1[2*i], y1[2*i]], i = 0 .. N)]);

epsilon:=(x0,h)->add((firsttest[i][2]-secondtest[i][2])^2 , i=1..round(x0/(2*h))+1)

end proc;