### A Runge-Kutta-4 Solution grapher for Differential Equations on the TI-82/83

#### -- a program --

This is for solving differential equations of the form dy/dx = (and expression in terms of x and y), such as dy/dx = xy2/5, that have a specific initial condition, such as y(1)=4. It uses the Runge-Kutta method of order 4. The solution curve is graphed, and the final value for y can be displayed.

The program is available in two formats.

• A screen shot for those typing in by hand.

•

#### Instructions:

1. Store the expression for dy/dx in Y1 on the [Y=] screen. (In the example above, Y1=XY^2/5)
2. Set the [WINDOW] as you desire.
3. Run the program RK4
1. Input the initial value for x as X START, the initial value for y as Y START.
2. Give a stopping-value of x as FINAL X
3. Give the desired number of steps as STEPS (note: more steps means better accuracy and slower program execution).
5. The solution curve is then graphed by the program
6. After the program stops, you can type X [ENTER][ALPHA]Y[ENTER] to see the final values of x and y.