Differential Equations - Numerical Solutions of Ordinary Differential Equations

1

Find the solutions to the second order boundary-value problem. , , $y\left(2\pi\right) = 1$ .

2

Find the solutions to the second order boundary-value problem. , , $y\left(2\pi\right) = 1$ .

3

Find the solutions to the second order boundary-value problem. , , $y\left(\frac{\pi}{2}\right) = 1$ .

4

Find the solutions to the second order boundary-value problem. , , $y\left(\frac{\pi}{2}\right) = 1$ .

5

The two-step Adams-Bashforth method of approximation uses the approximation scheme $y_{i+2} = y_{i+1} - \frac{1}{2}hf(t_i, y_i) + \frac{3}{2}hf(t_{i+1}, y_{i+1})$ .

Given that and , use the Adams-Bashforth method to approximate for with a step size of

6

The two-step Adams-Bashforth method of approximation uses the approximation scheme $y_{i+2} = y_{i+1} - \frac{1}{2}hf(t_i, y_i) + \frac{3}{2}hf(t_{i+1}, y_{i+1})$ .

Given that and , use the Adams-Bashforth method to approximate for with a step size of