ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 16 May 2019 03:16:22 -0500Derivative of a recurrence equationhttp://ask.sagemath.org/question/46543/derivative-of-a-recurrence-equation/Given:
var('β α γ t R')
c = function('c')
g = function('g')
f = function('f')
λ = function('λ')
suppose I define a function as
def U(l):
eq = 0
for i in range(l):
eq += (β^i)*(((c(t+i)+α*g(t+i))^(1-R))/(1-R))
return eq
How do I take the first order derivative w.r.t. `C_t` `C_t+1` and so forth?
I tried:
n = 2
L = U(n)
L.derivative(c(t))
without any luck.marco_repettoThu, 16 May 2019 03:16:22 -0500http://ask.sagemath.org/question/46543/Cannot solve differential equation (Lane-Emden equation) numericallyhttp://ask.sagemath.org/question/45696/cannot-solve-differential-equation-lane-emden-equation-numerically/Hi, my friends,
I tried to solve Lane-Emden equation, as model of white dwarf,
$$
\frac{d^2x}{dt^2} +\frac2 t \frac{dx}{dt} + x^n = 0, ~~~~ where ~~~~n=\frac 3 2
$$
and I have some troubles in sagemath.
I am using following code:
T = ode_solver()
def f_1(t,y): return [y[1],-2/t*y[1]-y[0]^(3/2)]
T.function = f_1
def j_1(t,y): return [[0, 1], [-3/2*y[1]^(1/2), -2/t], [0,2*y[1]/t^2]] #Jacobian matrix
T.jacobian = j_1
T.algorithm = "rk8pd"
T.ode_solve(y_0=[1,0], t_span=[0,10], num_points=1000)
f = T.interpolate_solution()
plot(f, 0, 10)
Above code is very similar of the example in sagemath reference: Van der Pol equation
Both equations (Lane-Emden and Van der Pol) are non-linear differential equation, therefore, are not easy to solve.
I don't know where comes to problem in above codes, can someone give me a help?
JohnJohn BaoThu, 07 Mar 2019 03:08:58 -0600http://ask.sagemath.org/question/45696/difference equationshttp://ask.sagemath.org/question/8067/difference-equations/Hello all,
I was wondering about SAGE capabilities in solving coupled systems of difference equations; I don't see any z-transform capabilities so I think this may not be possible yet.
Ruy LopezRuy LopezSun, 10 Apr 2011 07:43:46 -0500http://ask.sagemath.org/question/8067/