Ordinary Differential Equations

Solve a differential equation representing a predator/prey model using both ode23 and ode45. These functions are for the numerical solution of ordinary differential equations using variable step size Runge-Kutta integration methods. ode23 uses a simple 2nd and 3rd order pair of formulas for medium accuracy and ode45 uses 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 vertical xy-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 $\left(\mathit{x}+\mathit{L}\cos \theta ,\mathit{y}+\mathit{L}\sin \theta \right)$.

Use ode78 and ode89 to solve a celestial mechanics problem that requires high accuracy in each step from the ODE solver for a successful integration. Both ode45 and ode113 are unable to solve the problem using the default error tolerances. Even with more stringent error thresholds, ode89 performs best on the problem due to the high accuracy of the Runge-Kutta formulas it uses in each step.

Use ode23t to 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 $$M{u}^{\prime }=\varphi (u)$$. The problem includes a constant, singular mass matrix $\mathit{M}$.

Solve Burgers' equation using a moving mesh technique [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.