Forming a matrix using Euler's method and ODE

[jaobyccdee]

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?

 

[I like Serena]

Hi jaobyccdee!

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

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...

 

[jaobyccdee]

Thx!:)