Consider the example problem x = x 4y, y = x + y with the initial conditions x(0) = 1
Chapter 8, Problem 7(choose chapter or problem)
Consider the example problem x = x 4y, y = x + y with the initial conditions x(0) = 1 and y(0) = 0. Use the RungeKutta method to find approximate values of the solution of this problem on the interval 0 t 1. Start with h = 0.2 and then repeat the calculation with step sizes h = 0.1, 0.05, ... , each half as long as in the preceding case. Continue the process until the first five digits of the solution at t = 1 are unchanged for successive step sizes. Determine whether these digits are accurate by comparing them with the exact solution given in Eqs. (10) in the text.
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