Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Engineering Mathematics Numerical Methods
Consider the ODE \(\dot{x}\) = f(x, t) in R for a smooth function f. Consider a general second-order Runge-Kutta formula of the form x(t +h) = x(t) + w1hf(t, x) + w2hf(t + αf, x + βhf) + O(h3). Which of the following choice of (w1, w2, α, β) are correct
1
(1, \(\frac12\), \(\frac13\), \(\frac13\))
2
(\(\frac16\), \(\frac56\), \(\frac35\), \(\frac35\))
3
(0, 1, \(\frac12\), 1)
4
(\(\frac25\), \(\frac52\), \(\frac15\), \(\frac15\) )
5
Question Not Attempted