Approximate solution of the system v'=f(t,v) : odesolve

• If v is a vector of variables [x1,.., xn] and if f is given by a vector of expressions [e1,...,en] depending of t and of [x1,.., xn], if the init 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
  

  x'(t) = - y(t)

  y'(t) = x(t)

  
  input :
  odesolve([-y,x],t=0..pi,[x,y],[0,1])
  Output :
  [-1.79045146764e-15,-1]

• If f is a function from $\mathbb {R}$×$\mathbb {R}$ⁿ to $\mathbb {R}$ⁿ.
  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 $\mathbb {R}$ⁿ 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 :
  
  

  x'(t) = - y(t)

  y'(t) = x(t)

  
  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]]]