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The order of the differential equation is the highest order of derivative of the unknown function that appears in the differential equation. For example, an equation containing only first-order derivatives is a first-order differential equation, an equation containing the second-order derivative is a second-order differential equation, and so on.
In mathematics, and in particular in the theory of solitons, the Dym equation (HD) is the third-order partial differential equation u t = u 3 u x x x . {\displaystyle u_{t}=u^{3}u_{xxx}.\,} It is often written in the equivalent form for some function v of one space variable and time
In calculus, a branch of mathematics, the third derivative or third-order derivative is the rate at which the second derivative, or the rate of change of the rate of change, is changing. The third derivative of a function y = f ( x ) {\displaystyle y=f(x)} can be denoted by
When converted to an equivalent system of three ordinary first-order non-linear differential equations, jerk equations are the minimal setting for solutions showing chaotic behaviour. This condition generates mathematical interest in jerk systems. Systems involving fourth-order derivatives or higher are accordingly called hyperjerk systems. [1]
Third-order methods can be generically written ... (1996), Solving ordinary differential equations II: Stiff and differential-algebraic problems, Berlin, New York ...
This is a third-order non-linear ordinary differential equation which can be solved numerically, e.g. with the shooting method. With the solution for f {\displaystyle f} and its derivatives in hand, the Prandtl y {\displaystyle y} -momentum equation can be non-dimensionalized and rearranged to obtain the y {\displaystyle y} -pressure gradient ...
In physics, jerk is the third derivative of position, with respect to time. As such, differential equations of the form (..., ¨, ˙,) = are sometimes called jerk equations. It has been shown that a jerk equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal ...
Lie point symmetry is a concept in advanced mathematics.Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order to study the solutions of ordinary differential equations [1] [2] [3] (ODEs).