- #1

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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?

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- Thread starter jaobyccdee
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- #1

- 33

- 0

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?

- #2

I like Serena

Homework Helper

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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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