Difference between revisions of "Riccati equation"
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(Created page with "Let $\mathbb{T}$ be a time scale. The Riccati equation is the dynamic equation defined by $$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ where $p(t)+\mu...") |
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| − | Let $\mathbb{T}$ be a [[time scale]]. The Riccati equation is the [[dynamic equation]] defined by | + | Let $\mathbb{T}$ be a [[time scale]]. The Riccati equation is the nonlinear [[dynamic equation]] defined by |
$$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ | $$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ | ||
where $p(t)+\mu(t)z(t)>0$ for all $t \in \mathbb{T}^{\kappa}$. | where $p(t)+\mu(t)z(t)>0$ for all $t \in \mathbb{T}^{\kappa}$. | ||
Revision as of 21:49, 9 June 2015
Let $\mathbb{T}$ be a time scale. The Riccati equation is the nonlinear dynamic equation defined by $$z^{\Delta}(t) + q(t) + \dfrac{z^2(t)}{p(t)+\mu(t)z(t)}=0,$$ where $p(t)+\mu(t)z(t)>0$ for all $t \in \mathbb{T}^{\kappa}$.
