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anonymous
 5 years ago
how does eulers method of approximation work?
anonymous
 5 years ago
how does eulers method of approximation work?

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nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0There are two kinds of Euler approximations called explicit and implicit. The explicit is a bit faster but the implicit one is much more stable. What you do is approximating the solution to an initialvalue problem by piecewise affine functions. So explicit Euler is the easiest approximation method you can think of. Just calculate the elevation at the starting point, go a bit in that direction and take the resulting end point as the new starting point. Then repeat that step.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0so instead of going to x=0 you just step down a bit?

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Don't what you mean amistre... For implicit in each step you set up a system of linear equations which contains the elevation at the starting and at the end point.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0elevation at the starting point..whats that mean? go abit in that direction and take the end point..... whats that mean?

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0You have given a initial value problem \[f'(t) = F(t, f(t)),\; f(t_0) = y_0\] So the starting point is (t_0, y_0). Also you must choose a step size h, which then gives you the precision. The elevation at the starting point is \[f'(t_0) = F(t_0, y_0)\] So going in that direction you get the approximation \[f(t_0 + h) \approx y_0 + h\cdot F(t_0, y_0)\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ahhh... that sounds more like integration methods.... unless im mistaken :)

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Well yes, solving initialvalue problems / differential equations is a generalization of integration.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i was thinking more along the lines of the Newton stuff in the books finding roots and what nots. ok

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0Hehe, that explains the confusion ;)
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