mssivava wrote:
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;
eqn_3:diff(m(z),z,1)-t(z)=0;
eqn_4:diff(t(z),z,1)+p=0;
My initial conditions are u(0)=0, om(0)=0
My boundary conditons 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 system.
Thanks in advance
Here is the solution by Volker van Nek
Hi,
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
answers.
The boundary values you can use to eliminate the unknown m(0) and t(0).
(%i10) bc_1: subst(L,z,rhs(sol[1]))=0$
(%i11) bc_2: subst(L,z,rhs(sol[3]))=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
