MTH3007B Weekly Problems 2

Original Documents: Problem Sheet / [[My Handwritten Solutions / Provided Solutions

Vibes: …

Used Techniques:

• …

---

1.1. Predicting Error in Different Methods

Question

Assume you solve a differential equation, $y^{\prime }(t)=g(t,y(t))$, using the forward Euler method using a step size of $\Delta t=0.01$. Also assume the (global) error is exactly as in the linear regime and the error in $y(t_{\text{max}})$ is $0.04$.

1. What would the error be if $\Delta t=0.005$?
2. What would the error be if $\Delta t=0.005$ and Ralston is used, instead? Assume an error of $0.03$ for $\Delta t=0.01$.

…

---

Rest on Blackboard? Can’t see them yet, though.