| | 743 | == Boost.Numeric.Odeint == |
| | 744 | * '''Author(s):''' Karsten Ahnert, Mario Mulansky |
| | 745 | * '''Version:''' |
| | 746 | * '''State:''' |
| | 747 | * '''Last upload:''' 2010, April 27 |
| | 748 | * '''Links:''' [http://svn.boost.org/svn/boost/sandbox/odeint/ |
| | 749 | Boost Sandbox] [http://svn.boost.org/svn/boost/sandbox/odeint/libs/numeric/odeint/doc/html/index.html Documentation] |
| | 750 | * '''Categories:''' [#MathAndNumerics Math And Numerics] |
| | 751 | * '''Description:''' Odeint is a library for solving initial value problems (IVP) of ordinary differential equations. Mathematically, these problems are formulated as follows: x'(t) = f(x,t), x(0) = x0. x and f can be vectors and the solution is some function x(t) fullfilling both equations above. Numerical approximations for the solution x(t) are calculated iteratively. The easiest algorithm is the Euler-Scheme, where starting at x(0) one finds x(dt) = x(0) + dt*f(x(0),0). Now one can use x(dt) and obtain x(2dt) in a similar way and so on. The Euler method is of order 1, that means the error at each step is ~ dt[superscript 2]. This is, of course, not very satisfying, which is why the Euler method is merely used for real life problems and serves just as illustrative example. |
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