Category:Euler Method
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This category contains pages concerning Euler Method:
Consider the first order ODE:
- $(1): \quad y' = \map f {x, y}$ subject to the initial condition $\map y {x_0} = y_0$
where $\map f {x, y}$ is a continuous real function.
Let $\map y x$ be the particular solution of $(1)$.
For all $n \in \N_{>0}$, we define:
- $x_n = x_{n - 1} + h$
where $h \in \R_{>0}$.
Then for all $n \in \N_{>0}$ such that $x_n$ is in the domain of $y$:
- $y_{n + 1} = y_n + h \map f {x_n, y_n}$
is an approximation to $\map y {x_{n + 1} }$.
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Pages in category "Euler Method"
The following 3 pages are in this category, out of 3 total.