6. Prove that when the fourth-order Runge-Kutta method is applied to the problem Jr' 2 ix, the formula for advancing this solution will he so + is = [1 + M +91%.2 + gal)? + gh'i'pm T. [Continuation] Prove that the local truncation error in the preceding problem is 0&5}. Fourth-Order Runge-Kutta Method The higher-order Runge-Kutta formulas are very tedious to derive, and we shall not do so. The formulas are rather elegant, however, and are easily programmed once they have been derived. Here are the formulas for the classical fourth-order Runge- Kutta method: x (t + h) = x(1) +(F1+2F2 + 2F3 + F4) (8) where F1 = hf (t, x) F2 = hf ( 1 + } h, x + ; FI) F3 = hf (1 + z h, x + - F2) FA = hf ( 1 + h, x +F3) This is called a fourth-order method because it reproduces the terms in the Taylor series up to and including the one involving h*. The error is therefore O(h). Exact expressions for the h error term are available