5.16 Euler's method

5.16 Euler's method Quiz

IB Maths: Applications and Interpretation HL: Quiz

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5 questions, one answer each

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  1. 1. dydx=2x+y\frac{dy}{dx}=2x+y, y(0)=1y(0)=1, h=0.5h=0.5. Find y1y_1.

    • A. 22
    • B. 1.51.5
    • C. 0.50.5
    • D. 2.52.5

  2. 2. Which gives the next value in Euler's method for dydx=f(x,y)\frac{dy}{dx}=f(x,y)?

    • A. yn+1=yn+f(xn+1,yn+1)y_{n+1}=y_n+f(x_{n+1},y_{n+1})
    • B. yn+1=h f(xn,yn)y_{n+1}=h\,f(x_n,y_n)
    • C. yn+1=yn+h f(xn,yn)y_{n+1}=y_n+h\,f(x_n,y_n)
    • D. yn+1=yn+h f(xn+1,yn)y_{n+1}=y_n+h\,f(x_{n+1},y_n)

  3. 3. dydx=y\frac{dy}{dx}=y, y(0)=2y(0)=2, h=0.1h=0.1. Estimate y(0.2)y(0.2).

    • A. 2.422.42
    • B. 2.42.4
    • C. 2.22.2
    • D. 2.442.44

  4. 4. A student halves the step length in Euler's method. What is the most likely effect?

    • A. The estimate becomes exact
    • B. The estimate becomes less accurate
    • C. The method no longer works
    • D. The estimate becomes more accurate but needs more steps

  5. 5. dxdt=2y\frac{dx}{dt}=2y, dydt=−x\frac{dy}{dt}=-x, x0=2x_0=2, y0=1y_0=1, h=0.5h=0.5. Find (x1,y1)(x_1,y_1).

    • A. (3,−0.5)(3,-0.5)
    • B. (3,0)(3,0)
    • C. (4,−1)(4,-1)
    • D. (2,−1)(2,-1)

Quiz