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 m1 and m2 connected by a rod of length 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 θ with the horizontal and the coordinates of the first mass are (x,y). With this formulation, the coordinates of the second mass are (x+L cos θ,y+L sin θ).

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.

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 Mu′=ϕ(u). The problem includes a constant, singular mass matrix M.