Runge-Kutta method of order four is used to find the solution of the differential equation dy/dx=f(x); quad y(0)=0 with step size h. If the solution is y(h)=h[af(0)+bf(h/2)+cf(h)] then what are the values of a, b, c respectively?

Q64Section I (Objective (Q1–Q80))63 of 79

Numerical Analysis — identifying Simpson-rule weights in an RK4 formula

Runge-Kutta method of order four is used to find the solution of the differential equation

$\frac{dy}{dx}=f(x); \quad y(0)=0$

with step size $h$ . If the solution is

$y(h)=h\left[af(0)+bf\left(\frac{h}{2}\right)+cf(h)\right]$

then what are the values of $a$ , $b$ , $c$ respectively?

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