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 binary version that you can load directly into the graphlink program and download to your calculator. NOTE: If you have trouble downloading this, try holding the shift button on your keyboard when you click on the link.
  • A screen shot for those typing in by hand.



    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
    4. When asked for input:
      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.

    Last Modified December 8, 1998.
    Prof. Janeba's Home Page | Send comments or questions to: mjaneba< at >willamette.edu
    Department of Mathematics | Willamette University Home Page