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Forming a matrix using Euler's method and ODE

  • Thread starter jaobyccdee
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  • #1
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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(t0)==x0
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?
 

Answers and Replies

  • #2
I like Serena
Homework Helper
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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...
 
  • #3
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Thx!!:)
 

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