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Forming a matrix using Euler's method and ODE

  1. Oct 25, 2011 #1
    L is the operator. Lx=x'(t)+u(t) x(t) =0. Provided that x(t0)=x0.
    Before writing the matrix. The book express it out in equations.
    x(t1)-x(t0)+Δt u(t0) x(t0)==0
    x(t2)-x(t1)+Δt u(t1) x(t1)==0
    Euler's method is x(t0)+Δt f[x0,t0], right?
    so where did the x'(t) from the original ODE goes?
  2. jcsd
  3. Oct 25, 2011 #2

    I like Serena

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    Hi jaobyccdee! :smile:

    Euler's method is [itex]x(t_{n+1}) = x(t_n) + \Delta t f(x_n, t_n)[/itex], where [itex]f(x_n, t_n) = x'(t_n)[/itex].

    With Lx=x'(t)+u(t) x(t) =0, it follows that x'(t)=-u(t) x(t).

    Substitute, rewrite the equation, and your equations should follow...
  4. Oct 25, 2011 #3
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