4.2: Example - the exponential growth ODE and error scaling
- Page ID
- 219159
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As usual, we examine the result of using Heun’s method on the exponential growth ODE, (eq:2.5). Simulation results are shown in fig. 4.2. The computed solution clearly gives a better match to the analytic results – Heun’s method is a better method than forward Euler!
We can quantify the accuracy of Heun’s method by computing the RMS error between the computed and the analytic solutions for different stepsizes \(h\). This is shown in 4.3. On a log-log plot the slope of the error line is two – the order of Heun’s method is accordingly \(O(h^2)\). That is, if we halve the stepsize then we get a factor of four improvement in method accuracy. This is much better than the \(O(h)\) accuracy offered by forward Euler.
