Solve a differential equation representing a predator/prey model using bothode23andode45．These functions are for the numerical solution of ordinary differential equations using variable step size Runge-Kutta integration methods.ode23uses a simple 2nd and 3rd order pair of formulas for medium accuracy andode45uses a 4th and 5th order pair for higher accuracy.

Solves a system of ordinary differential equations that model the dynamics of a baton thrown into the air [1]. The baton is modeled as two particles with masses ${\mathit{m}}_1$and ${\mathit{m}}_2$connected by a rod of length $\mathit{L}$．The baton is thrown into the air and subsequently moves in the verticalxy-plane subject to the force due to gravity. The rod forms an angle $\theta$with the horizontal and the coordinates of the first mass are $\left(\mathit{x},\mathit{y}\right)$．With this formulation, the coordinates of the second mass are $\left(\mathit{x}+\mathit{L}\cos \theta ,\mathit{y}+\mathit{L}\sin \theta \right)$．

Useode78andode89to solve a celestial mechanics problem that requires high accuracy in each step from the ODE solver for a successful integration. Bothode45andode113are unable to solve the problem using the default error tolerances. Even with more stringent error thresholds,ode89performs best on the problem due to the high accuracy of the Runge-Kutta formulas it uses in each step.

Useode23tto solve a stiff differential algebraic equation (DAE) that describes an electrical circuit [1]. The one-transistor amplifier problem coded in the example file amp1dae.m can be rewritten in semi-explicit form, but this example solves it in its original form $$M{u}^{\prime }=\varphi (u)$$．这一问题包括一个常数,单一的质量atrix $\mathit{M}$．

使用动网格技术解决汉堡的方程que [1]. The problem includes a mass matrix, and options are specified to account for the strong state dependence and sparsity of the mass matrix, making the solution process more efficient.