Ad
related to: third order differential equation
Search results
Results From The WOW.Com Content Network
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.
Third-order methods can be generically written ... (1996), Solving ordinary differential equations II: Stiff and differential-algebraic problems, Berlin, New York ...
In mathematics, the Chazy equation is the differential equation = (). It was introduced by Jean Chazy (1909, 1911) as an example of a third-order differential equation with a movable singularity that is a natural boundary for its solutions.
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
Third-order differential equations of the form (..., ¨, ˙,) = are sometimes called jerk equations. 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 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 ...
High-order compact finite difference schemes are used for solving third-order differential equations created during the study of obstacle boundary value problems. They have been shown to be highly accurate and efficient. They are constructed by modifying the second-order scheme that was developed by Noor and Al-Said in 2002.
For arbitrary stencil points and any derivative of order < up to one less than the number of stencil points, the finite difference coefficients can be obtained by solving the linear equations [6] ( s 1 0 ⋯ s N 0 ⋮ ⋱ ⋮ s 1 N − 1 ⋯ s N N − 1 ) ( a 1 ⋮ a N ) = d !