Differential Equations for Engineers
Some analysis (not shown here) on the second-order Runge-Kutta methods results in the constraints a +b = 1, ab = bb = 1/2. Write down the second-order Runge-Kutta methods corresponding to (i) a = b, and (ii) a = 0. These specific second-order Runge-Kutta methods are called the modified Euler method and the midpoint method, respectively.
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