If v is a vector
of variables [x1,..,xn] and if f is given by a vector of expressions
[e1,...,en] depending on t and of [x1,..,xn],
if the initial value of v at t0
is the vector [x10,...,xn0] then the instruction
odesolve([e1,..,en],t=t0..t1,[x1,...,xn],
[x10,...,xn0])
returns an approximated value of v at t=t1.
With the optional argument curve, odesolve returns the list of
the intermediate values of [t,v(t)] computed by the solver. Example, to solve the system
Input :
odesolve([-y,x],t=0..pi,[x,y],[0,1])
Output :
[-1.79045146764e-15,-1]
If f is a function from ℝ × ℝn to
ℝn.
odesolve(t0..t1,(t,v)->f(t,v),v0) or
odesolve(t0..t1,f,v0)
computes an approximate value of v(t1) where the vector v(t)
in ℝn is the solution of
v′(t)=f(t,v(t)), v(t0)=v0 |
With the optional argument curve, odesolve returns the list of
the intermediate value [t,v(t)] computed by the solver.Example, to solve the system :
Input :
odesolve(0..pi,(t,v)->[-v[1],v[0]],[0,1])
Or define the function:
f(t,v):=[-v[1],v[0]]
then input :
odesolve(0..pi,f,[0,1])
Output :
[-1.79045146764e-15,-1]
Alternative input :
odesolve(0..pi/4,f,[0,1],curve)
Output :
[[0.1781,[-0.177159948386,0.984182072936]], [0.3781,[-0.369155338156,0.929367707805]], [0.5781,[-0.54643366953,0.837502384954]], [0.7781,[-0.701927414872,0.712248484906]]]