Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in or
create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision |
Your text |
Line 546: |
Line 546: |
| ==== Problem ==== | | ==== Problem ==== |
|
| |
|
| When using lsode or other ODE solver to find the state variables x as a function of time t in a set of ODE's, there seems to be no simple way to return and tabulate algebraic variables y that are a function of the state variables x and time t, other than the derivatives. | | When using lsode or other ODE solver to find the state variables x as a function of time t in a set of ODE's, there seems to be no way to tabulate algebraic variables y that are a function of the state variables x and time t. |
| | |
| Consider a modified version of the spring function defined above in the section on parametric functions:
| |
| | |
| <syntaxhighlight lang="Octave">
| |
| function sprime=dspring (s, t)
| |
| k=1;
| |
| tau=1;
| |
| x = s(1);
| |
| v = s(2);
| |
| y=x+v*tau;
| |
| sprime(1) = v;
| |
| sprime(2) = -k * y;
| |
| endfunction
| |
| </syntaxhighlight>
| |
| | |
| What would be a way to way to use this function and lsode to tabulate not just the elements of x and sprime, but also (say) y as a function of time?
| |
|
| |
|
| ==== Solution ==== | | ==== Solution ==== |
| | | UNDER CONSTRUCTION |
| Modify the function sprime to return y as a second argument:
| |
| | |
| <syntaxhighlight lang="Octave">
| |
| function [sprime,y]=dspring (s, t)
| |
| k=1;
| |
| tau=1;
| |
| x = s(1);
| |
| v = s(2);
| |
| y=x+v*tau;
| |
| sprime(1) = v;
| |
| sprime(2) = -k * y;
| |
| endfunction
| |
| </syntaxhighlight>
| |
| | |
| lsode will happily ignore the second return argument y, but after x has been tabulated, y can be tabulated using the second return argument of the spring function in a for loop, e.g.
| |
| | |
| <syntaxhighlight lang="Octave">
| |
| t = linspace (0, 10, 100);
| |
| x = lsode ('dspring',[1;0], t);
| |
| y=zeros(length(t),1);
| |
| for i=1:length(t)
| |
| [xtmp,y(i,1)]=dspring(x(i,:),t(i));
| |
| end
| |
| </syntaxhighlight>
| |
| | |
|
| |
|
| ==== Discussion ==== | | ==== Discussion ==== |
| | | UNDER CONSTRUCTION |
| This is a simple example with one algebraic variable. Others can be added by extending the second dimension of the y array.
| |
|
| |
|
| [[Category:Examples]] | | [[Category:Examples]] |