Match the problem type in Group-$1$ with the numerical method in Group-$2$.

$\begin{array}{cc}\ &\text{Group-$1$} & \text{Group-$2$} \\ &\text{P. System of linear algebraic equations} & \text{ I. Newton-Raphson} \\ &\text{Q. Non-linear algebraic equations} & \text{II. Gauss-Seidel} \\ &\text{R. Ordinary differential equations} & \text{III. Simpson’s rule} \\ &\text{S. Numerical integration} & \text{IV. Runge-Kutta}\\ \end{array}$

Choose the correct set of combination.

1. $P-II,\:Q-I,\:R-III,\:S-IV$
2. $P-I,\:Q-II,\:R-IV,\:S-III$
3. $P-IV,\:Q-III,\:R-II,\:S-I$
4. $P-II,\:Q-I,\:R-IV,\:S-III$