TI-92 Help -- Numerical Solutions of Differential Equations

y'' = f(t, y, y')

The basic idea behind the numerical solution of a second order differential equation of the form

y'' = f(t, y, y')

is that this single equation can be expressed as a system of two first order equations. We introduce a new variable v for y' and then notice that v' = y'' so that we can express the equation above as


v' = f(t, y, v)
y' = v

Here are some examples


- - - - - - - - - - - - - - - - - - - - - - - - - - - -

y'' = -3 y              becomes    v' = -3 y
                                   y' = v
- - - - - - - - - - - - - - - - - - - - - - - - - - - -

y'' = -y' - 4y          becomes    v' = -v - 4y
                                   y' = v
- - - - - - - - - - - - - - - - - - - - - - - - - - - -

y'' = -y' - 4y + sin t  becomes    v' = -v - 4y + sin t
                                   y' = v

- - - - - - - - - - - - - - - - - - - - - - - - - - - -

Once the original second order equation has been rewritten in this way as a system of two first order equations the method used for working with a system of two equations of the form


x' = f1(t, x, y)
y' = f2(t, x, y)

can be used. Click here to go to the appropriate TI-92 help module.