23.4.2  Approximating solutions of the system v′=f(t,v)

This section covers using odesolve to solve first order systems of differential equations; using it to solve a single first order differential equation was discussed last section.

The odesolve can be used to solve a system of the form

where x=[x₁,…,x_n] is a list of unknown functions and f is a function of n+1 variables with an initial condition.

odesolve can take its arguments in various ways. Letting t be the independent variable and x=[x₁,…,x_n] be a vector of dependent variables, t₀ and x₀ be the initial values, t₁ the place where you want the value of x, f be the function in the differential equation, f(t,x) be a list of expressions which determines the function f (see Section 8.2.1 for the difference between a function and an expression).

• odesolve takes three or four mandatory arguments and two optional arguments:
  • mandatory, mandatory arguments given by one of the following sequences:
    • f(t,x),t=t₀..t₁,x,x₀
    • t₀..t₁,(t,y)↦ f(t,y),x₀
    • t₀..t₁,f,x₀
  • Optionally, curve, the symbol.
• odesolve(mandatory ⟨,curve ⟩) returns an approximate value of x(t₁) with x being the particular solution of x′(t)=f(t,x(t)) statisfying the initial condition x(t₀)=x₀. With an optional argument of curve, the list of all the [t,[x(t)]] values that were computed by the solver are returned.

Examples

Solve the system of equations x′(t)=−y(t) and y′(t)=x(t):

Solve the system of equations x′(t)=−y(t) and y′(t)=x(t):

or: