Items tagged with ode ode Tagged Items Feed

Hello!

Could you pleasу tell me, is it possible to make MapleSim not to simplify equation set of my model and solve equations without simplification? I want to do this because simplification process (reduction of equations number) takes too much time in comparison with integration process.

Thank you!

method=laplace???...

October 19 2011 kh2n 215

Hi,

 

Can i use method=laplace to solve an ode with no initial condition?

 

ode := diff(phi2(x),`$`(x,2))-Omega0*diff(phi2(x),x)-k*R1*E1/C*sigma*phi2(x)-l^2*phi2(x)+2*R*k/C*N2*exp(Omega0*(x-1))*cosh(l*(x-1))*l*C2/exp(-l) = 0;

bcs:=phi2(1)=0,phi2(S0)=-N4*Phi;

sol := dsolve({ode, bcs}, phi2(x), method=laplace);

 

Thanks

sc_vs_t.mw

sc_vs_t.pdf

 

I want the solution of an ODE for different values of d say d=3,4,5,6... etc (see the mw file). I want to plot a(t) vs t for these different values of d.

Now what is wrong with my code ?  How to fix it ? 

I also  added a Mathematica work of the same thing (see the pdf) ,...

fsolve float issue...

September 27 2011 goli 130

Dear guys, Can anyone tell me why my program does not work for some initial values? All my equations are:

> alpha := (6*h^2)^(1-n)*(1-k)^(1-n)*((1-m+k)/(2*n-1-k));

> eq := z-> 1=(m*(1+z)^3-k*(1+z)^2)*h^2/(H^2)+(((2*n-1)-(k*(1+z)^2*h^2/H^2))*((1-m+k)/(2*n-1+k))*((((H^2/h^2)-k*(1+z)^2)/(1-k))^(n-1)));

> Y := z->if not type(z,numeric) then 'procname(z)' else (fsolve(eq(z), H=h)) end if;

> l := dsolve({D(L)(z) = L(z)/(1+z)+(1+z...

hi all,

To create an observability grammian I have to integrate a matrix with some equations that are difficult to integrate due to multiple time dependent variables. The simplest expression in the matrix is:

z1^2 * sin( z5 * t)^2          (1)

where z1 and z5 are from a state space model with 5 states and are given by:

z1dot = z2     ...

Hi,

I have what I hope is an easy problem to answer. How would one go about having Maple solve a "vectorized" initial-value problem. For example,

 y'(t) =[t^2,exp(t)], y(0)=[-1,1]. Find y(t).

 Thanks!

Hi there,

I have a de that I have gotten maple to solve using dsolve (y'''+2y''-11y'-12y)=48-28exp(3t). When the solution comes up however, the particular solution is in an odd form: 

(-4*exp(3*t)+(11/28)*exp(6*t)-t*exp(6*t))*exp(-3*t)

+_C1*exp(-4*t)+_C2*exp(-t)+_C3*exp(3*t)

However, the particular solution here contains part of the homogeneous solution inside of it: namely the 11/28exp(3t) term. Is there any way to run a function on my solution...

My question is related to this discussion on "querying events"

http://www.mapleprimes.com/questions/125273-Dsolve-Events-How-To-Control-For-A-Sign-Change#comment125426

I thought I might start a new thread.

The following loop is an illustration of the sort of thing I'd like to do with dsolve and events: I loop over a parameter of the "event" and extract information on the solution at different values of the parameter. Here is the code (successfully tested on Maple 15 / Standard / Windows)...

hi

 

i write the following code

> restart;
>
nn:=2;
NB:=0.5;
Le:=2;
Pr:=2;
b:=13;

aa:=-0.2;
                              -0.2

for iu from 0 by 1 to 20 do
Nt:=aa+0.2;
sol := dsolve({diff(G(x), x, x)+Le*f(x)*(diff(G(x), x))+(Nt/NB)*diff(T(x), x, x...

hi

i have written the following code but it not converge. how can i do?

 

> restart;
>
nn:=2;
Nt:=0.5;
NB:=0.5;
Le:=0.5;
Pr:=2;
b:=18;

 sol := dsolve({diff(G(x), x, x)+Le*f(x)*(diff(G(x), x))+(Nt/NB)*diff(T(x), x, x) = 0,diff(f(x), x, x, x)+f(x)*(diff(f(x), x, x))-(2*nn)/(nn+1)*(diff(f(x), x))^2 = 0,diff(T(x), x, x)/Pr+f(x)*(diff(T(x), x))+NB*(diff(T(x), x))*(diff(G(x), x))+Nt*(diff(T(x), x))^2=0,G(0) = 1, G(b...

hi

 

i write a code that solve system of ode. when i ask maple to show my answer its shows following statement:

 sol := dsolve({diff(G(x), x, x)+Le*f(x)*(diff(G(x), x))+(Nt/NB)*diff(T(x), x, x) = 0,diff(f(x), x, x, x)+f(x)*(diff(f(x), x, x))-(2*nn)/(nn+1)*(diff(f(x), x))^2 = 0,diff(T(x), x, x)/Pr+f(x)*(diff(T(x), x))+NB*(diff(T(x), x))*(diff(G(x), x))+Nt*(diff(T(x), x))^2=0,G(0) = 1, G(b) = 0, T(0) = 1, T(b) = 0, f(0) = 0, (D(f))(0) = 1, (D(f))(b) = 0}, numeric);

And so with this provocative title, "pushing dsolve to its limits" I want to share some difficulties I've been having in doing just that. I'm looking at a dynamic system of 3 ODEs. The system has a continuum of stationary points along a line. For each point on the line, there exist a stable (center) manifold, also a line, such that the point may be approached from both directions. However, simulating the converging trajectory has proven difficult.

I have simulated as...

I'm currently trying to solve a set of ODE's using dsolve/numeric and I'm unsure about the result I'm getting.  Some help with the worksheet and general help with the solution method would be appreciated.

 

Here are the equations:

 diff(b1(t), t) = I*u1(t)

I use rk4 to solve this equation with the paramater w = 500, I want to get the numbers of steps.

And when I change the parameter w = 1000, I want to obtain the numbers ofsteps?

Here is the procedure:

restart:
Digits:= 32;
w :=  500;
ode := diff(y(t), `$`(t, 1)) = 2*I*y(t) + sin(w*t)*y(t)*y(t):
ics := y(0) = 1:

p2 := dsolve({ics, ode}, numeric, method = classical[rk4]):

 

Thanks for your help.

I have a set of nonlinear and coupled PDEs for a cable actuated system. I want to transfer this set to a set of ODEs and write it down in Matrix form. I used Galerkin's method and derived the ODEs in discritized form. I have a problem in converting this set of equation into a matrix form like "Mq"+Cq'+Kq=F". The derived equations are very complicated and contains some nonlinear terms. One of the three equations looks like this:

 

First 9 10 11 12 13 14 15 Page 11 of 16