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→Find Algebraic Variables from ODE State Variables
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==== 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 way to tabulate algebraic variables y that are a function of the state variables x and time t. | 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. | ||
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 ==== | ||
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 ==== | ||
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]] | ||