desolve_system where boundary values are functions of the dependent variable

asked 2012-06-06 10:37:32 +0100

Daniel Farrell
3 ●1 ●1 ●4

updated 2012-06-06 10:40:07 +0100

I am using desolve_system() to solve a boundary value problem. The equations are very simple but I'm having a bit of difficulty trying to include the boundary conditions. The system of equations and boundary conditions are,

System of differential equations with boundary values.

This is the code that I'm using in sage. How can I include the boundary values in this problem?

reset()
var('I_1 I_2 I0 R0 R1 x alpha D')
I_1 = function('I_1', x)
I_2 = function('I_2', x)
eq1 =  diff(I_1,x) == -alpha * I_1
eq2 = -diff(I_2,x) == -alpha * I_2
sol = desolve_system( [eq1, eq2], [I_1, I_2], ivar=x)
view(sol)
# How can I include these?
#BV1: I_1(x=0)==A*I_2(x=0) + C
#BV2: I_2(x=D)==B*I_1(x=D)

edit retag flag offensive close merge delete

add a comment

reset() var('I_1 I_2 I0 A B C D c c1 c2 x alpha D') I_1 = function('I_1', x) I_2 = function('I_2', x) eq1 = diff(I_1,x) == -alpha * I_1 eq2 = -diff(I_2,x) == -alpha * I_2 sol1 = desolve( eq1,I_1,ivar=x) sol2 = desolve( eq2,I_2,ivar=x) sol1=sol1.subs(c=c1) sol2=sol2.subs(c=c2) e1=sol1.subs(x=0)==A*sol2.subs(x=0)+C e2=sol2.subs(x=D)==B*sol1.subs(x=D) sol=solve([e1,e2],[c1,c2]) print "I_1 =",sol1.subs(sol[0][0]) print "I_2 =",sol2.subs(sol[0][1]) #I_1 = -C*e^(2*D*alpha - alpha*x)/(A*B - e^(2*D*alpha)) #I_2 = -B*C*e^(alpha*x)/(A*B - e^(2*D*alpha))

Comments

Thank you very much, that's a very clever solution.

Daniel Farrell ( 2012-06-06 22:16:49 +0100 )edit

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

desolve_system where boundary values are functions of the dependent variable

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

desolve_system where boundary values are functions of the dependent variable edit

1 Answer

Comments

Your Answer

Question Tools

Stats

Related questions

desolve_system where boundary values are functions of the dependent variable