Euler's methods for differential equationsAQA A-Level Further Maths: Mind map

Exam questions on Euler's methods for differential equations

1. A curve satisfies $\frac{dy}{dx}=x+y$ with $y=1$ when $x=0$. Use a step length $h=0.1$.
   Using $y_1=1.1$ from Euler's method, use the improved Euler method to estimate $y$ when $x=0.2$.2 marks
2. A curve satisfies $\frac{dy}{dx}=x^2-y$ with $y=2$ when $x=1$. Use Euler's method with step length $h=0.2$.
   Explain why a smaller value of $h$ usually gives a more accurate estimate, and state the cost of using it.2 marks
3. A cooling object has temperature $T$ °C at time $t$ minutes, where $\frac{dT}{dt}=-0.1(T-20)$ and $T=80$ when $t=0$. Euler's method with step length $h=2$ minutes is used.
   Use Euler's method to estimate $T$ when $t=2$ and when $t=4$.3 marks