Differential Equations in Spreadsheets: Euler, Heun & Runge–Kutta Methods

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Compute a slope field for dy/dt = a·t − b·y and test whether a candidate function really solves the equation.
• Solve Newton's law of cooling with Euler steps of 2 minutes, compute the exact solution next to it and measure the error.
• Run Euler for a growing culture with six step sizes, measure the error and read off the order of the method.
• Solve the cooling coffee again with 3-minute steps, now with Heun's predictor–corrector method, and compare its error with Euler's.
• Write one classical RK4 step for logistic growth in a pond, let the table repeat it for 20 months and compare with the exact solution.
• Step two coupled equations for hares and lynxes forward with Euler's method and chart the cycles of both populations.
• Rewrite m·x″ + c·x′ + k·x = 0 as two first-order equations, step a damped spring with Euler's method and chart it against the exact solution.
• Find the step sizes for which Euler is stable on a stiff equation, compute the critical step and solve the problem with the backward (implicit) Euler method instead.