Josephood7

solutions are put in notion, check out the link below

notion：

https://www.notion.so/hw5-Numerical-Analysis-f678a2657f7c43f593100c6bf1948ee8

Part A. (50%) A.1 Plot the stability diagram for the second-order Runge-Kutta method. Where does the neutral curve intersect with Re(λh)? A.2 Plot the stability diagram for the fourth-order Runge-Kutta method. Where does the neutral curve intersect with Re(λh) and with Im(λh)?

Part B. (50%) Consider the equation dy dx + (2 + 0.01x 2 )y = 0, subject to y(0) = 4 in the range 0 ≤ x ≤ 15. B.1 Solve this equation using the following numerical schemes: i) Euler, ii) backward Euler, iii) trapezoidal, iv) second-order Runge-Kutta and v) fourth-order Runge-Kutta. Use ∆x = 0.1, 0.5, 1.0 and compare to the exact solution. B.2 For each scheme, estimate the maximum ∆x for stable solution over the given domain and discuss your estimate in terms of results of B.1.