Differential equations system solving with boundaries
asked 2017-02-28 09:35:18 -0500
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being a newbie in the practice of Sage I hope this question won't be silly, but unfortunately I cannot find anything helpful in the the forum neither in the documentation.
I am handling a system of 6 differential equations as follows, using
var ('t a b c d e g') a = function('a')(t) b = function('b')(t) c = function('c')(t) d = function('d')(t) e = function('e')(t) g = function('g')(t) dea = diff(a,t) == -10*a + 2*b + 3*c + 3*d + 2*e + 5*g deb = diff(b,t) == -9*b + e dec = diff(c,t) == -9*c + d + e ded = diff(d,t) == -9*d + 2*a + 2*b + 2*c + 3*e + 2*g dee = diff(e,t) == -10*e deg = diff(g,t) == -9*g + 9*a + 2*b + 3*c + 3*d + 3*e sol = desolve_system([dea, deb, dec, ded, dee, deg], [a,b,c,d,e,g], ics=[0,1,1,1,1,1,1]) f(t,a,b,c,d,e,g) = sol f = f(t) var('sola,solb,solc,sold,sole,solg') sola=f.rhs() solb=f.rhs() solc=f.rhs() sold=f.rhs() sole=f.rhs() solg=f.rhs()
The thing goes fine and solutions are provided. However, I need and extra boundary condition which is necessary for properly solving the problem (which is related to chemical kinetics, BTW, hence some conditions are mandatory for heading to a physical meaning of the solutions), i.e.:
a + b + c + d + e + g == 6
However, I cannot understand from the on line manual and its examples how to handle this condition, but I am only able to impose the initial conditions a0 = 1, b0 = 1 etc ... Could anyone suggest a possible solution to my problem and/or the good syntax for imposing such conditions to my equations?
Thanks in advance.