[Maxima] a problem with linear system of 4 differential equation
van.nek at arcor.de
Mon Aug 25 14:44:09 CDT 2008
it is quite normal also to send a copy of your response to the mailing list. So the other
participiants might be interested in your answer.
There are different ways to define a function. Use e.g.
foo(z) := 3*z^2+5$
if the right side of this definition is explicitely given. Maxima doesn't evaluate here.
In your example you want to pull out an expression from an equation inside of a list. So
evaluation is needed. In this case you might want to use define. The result shows the
explicite := definition.
(%i15) --> see my previous post below
(%i16) define(u(z), rhs(sol));
u(z) := ''( rhs(sol );
would do the same (two single quotes!)
Now you can use the function definition to prove the boundary condition.
Welcome to Maxima
Volker van Nek
Am 25 Aug 2008 um 21:46 hat mssivava mssivava geschrieben:
> Hi Volker,
> I calculated with mathematica also. And the result is the same with your code. Thank you very
> much for your kind attention. You helped me so much.
> If I don't disturb you, may I ask one more question? How can I take for example u(z) from the
> 2008/8/25, van Nek <van.nek at arcor.de>:
> the function desolve can solve your initial value problem. View documentation by typing
> ? desolve
> for more examples. And there is a chapter on differential equations in the manual.
> (%i1) display2d:false$
> (%i2) eqn_1: 'diff(u(z),z,1)+om(z)=0$
> (%i3) eqn_2: 'diff(om(z),z,1)-m(z)/d-(gam^2*p/d)=0$
> (%i4) eqn_3: 'diff(m(z),z,1)-t(z)=0$
> (%i5) eqn_4: 'diff(t(z),z,1)+p=0$
> (%i6) atvalue(u(z),z=0,0)$
> (%i7) atvalue(om(z),z=0,0)$
> (%i8) sol: desolve([eqn_1,eqn_2,eqn_3,eqn_4], [u(z),om(z),m(z),t(z)])$
> (%i9) sol: ratsimp(sol)$
> For better readability I omit Maxima's response here. By replacing the $ by ; you'll see the
> The boundary values you can use to eliminate the unknown m(0) and t(0).
> (%i10) bc_1: subst(L,z,rhs(sol))=0$
> (%i11) bc_2: subst(L,z,rhs(sol))=0$
> (%i12) sol: eliminate(append(sol,[bc_1,bc_2]),[m(0),t(0)])$
> (%i13) sol: solve(sol,[u(z),om(z),m(z),t(z)])$
> L is introduced. I declare z to be the main variable and simplify.
> (%i14) declare(z,mainvar)$
> (%i15) sol: ratsimp(sol)$
> I hope you like the result.
> Volker van Nek
> Am 25 Aug 2008 um 8:26 hat mssivava geschrieben:
> > Hi everyone, I have 4 linear system of differential equations which are
> > eqn_1:diff(u(z),z,1)+om(z)=0; eqn_2:diff(om(z),z,1)-m(z)/d-(gam^2*p/d)=0;
> > t(z)=0; eqn_4:diff(t(z),z,1)+p=0; My initial conditions are u(0)=0, om(0)=0 My boundary
> > are u(L)=0, m(L)=0 I would like to find u(z), om(z), m(z) and t(z) So, I tried to use desolve
> > function to solve this equation system. But I couldn't. Can anyone help me to solve this
> > Thanks in advance
> > View this message in context: a problem with linear system of 4 differential equation
> > Sent from the Maxima mailing list archive at Nabble.com.
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