Difference between revisions of "Integrators for time stepping"
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Numerically, we usually choose a time step \Delta t and integrate the function up to a certain time t_{\max}. Times os subsequent time steps are denoted with t_i and function values with y_i. | Numerically, we usually choose a time step \Delta t and integrate the function up to a certain time t_{\max}. Times os subsequent time steps are denoted with t_i and function values with y_i. | ||
| − | The simplest method is explicit Euler's method | + | The simplest method is explicit Euler's method: |
y_{n+1} = y_{n} + \Delta t f(t, y_n) | y_{n+1} = y_{n} + \Delta t f(t, y_n) | ||
| + | |||
| + | = Explicit methods = | ||
Revision as of 12:52, 10 November 2017
Integrators for time stepping
We are solving an initial value problem, given as
\begin{align*} \dot{y}(t) &= f(t, y) \\ y(t_0) &= y_0 \end{align*}
where y is the unknown (possibly vector) function, t_0 is the start time, f is the derivative (the functions we wish to integrate) and y_0 is the initial value of y. Numerically, we usually choose a time step \Delta t and integrate the function up to a certain time t_{\max}. Times os subsequent time steps are denoted with t_i and function values with y_i.
The simplest method is explicit Euler's method: y_{n+1} = y_{n} + \Delta t f(t, y_n)
