Consider the following initial value problem x' = 2x^2 + x - 1, x(1) = 1. (a) Write out Euler's method for this ODE. Compute the value of x(1.2) using Euler's method, with h = 0.1.
(b) Write out the Heun's method for this ODE. Compute the value x(1.2) by Heun's method, with h = 0.1.
(c) Write out the classic 4-th order Runge-Kutta method for this ODE. Compute the value x(1.2) by 4-th order Runge-Kutta method, with h = 0.1.
(d) Write out the 2-nd order Adams-Bashforth-Moulton method for this ODE. Note that this is a multi-step method. It needs 2 initial values, i. e., x0 and x1, to initiate the iterations. For the second initial value x1, you can use the result obtained in part (b) with Heun's method. Compute the values x(1.2) and x(1.3) using the ABM method