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ode_system [2013/09/16 22:55] nikolaj |
ode_system [2015/03/27 20:14] nikolaj |
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===== ODE system ===== | ===== ODE system ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $ d,n,m,k\in\mathbb N $ | | + | | @#55CCEE: context | @#55CCEE: $ d,n,m,k\in\mathbb N $ | |
- | | @#88DDEE: $ F:\mathbb R\times\mathbb R^{d\ \cdot\ (1+n)}\to \mathbb R^m $ | | + | | @#55CCEE: context | @#55CCEE: $ F:\mathbb R\times\mathbb R^{d\,(1+n)}\to \mathbb R^m $ | |
- | | @#88DDEE: $ B:\mathbb R^d\to \mathbb R^k $ | | + | | @#FFBB00: definiendum | @#FFBB00: $ y \in $ it | |
+ | | @#55EE55: postulate | @#55EE55: $ y:C^k(\mathbb R,\mathbb R^d) $ | | ||
+ | | @#55EE55: postulate | @#55EE55: $ F(t,y(t),y'(t),y''(t),\dots,y^{(n)}(t))=0 $ | | ||
- | | @#FFBB00: $ y $ | | + | ----- |
- | + | ||
- | | @#55EE55: $ y:C^k(\mathbb R,\mathbb R^d) $ | | + | |
- | + | ||
- | | @#55EE55: $ F(t,y(t),y'(t),y''(t),\dots,y^{(n)}(t))=0 $ | | + | |
- | | @#55EE55: $ B(y)=0 $ | | + | |
- | + | ||
- | ==== Discussion ==== | + | |
- | ==== Parents ==== | + | |
=== Reference === | === Reference === | ||
Wikipedia: [[https://en.wikipedia.org/wiki/Ordinary_differential_equation|Ordinary differential equation]] | Wikipedia: [[https://en.wikipedia.org/wiki/Ordinary_differential_equation|Ordinary differential equation]] | ||
- | === Suset of === | + | |
+ | ----- | ||
+ | === Subset of === | ||
[[PDE system]] | [[PDE system]] |