  In this work we present Haar wavelet collocation method and solve the
following class of system of Lane-Emden equation defined as \begin{eqnarray*}
-(t^{k_1} y'(t))'=t^{-\omega_1} f_1(t,y(t),z(t)),\\ -(t^{k_2}
z'(t))'=t^{-\omega_2} f_2(t,y(t),z(t)), \end{eqnarray*} where $t>0$, subject to
initial values, boundary values and four point boundary values:
\begin{eqnarray*} \mbox{Initial
Condition:}&&y(0)=\gamma_1,~y'(0)=0,~z(0)=\gamma_2,~z'(0)=0,\\ \mbox{Boundary
Condition:}&&y'(0)=0,~y(1)=\delta_1,~z'(0)=0,~z(1)=\delta_2,\\
\mbox{Four~point~Boundary~Condition:}&&y(0)=0,~y(1)=n_1z(v_1),~z(0)=0,~z(1)=n_2y(v_2),
\end{eqnarray*} where $n_1$, $n_2$, $v_1$, $v_2$ $\in (0,1)$ and $k_1\geq 0$,
$k_2\geq0$, $\omega_1<1$, $\omega_2<1$ are real constants. Results are compared
with exact solutions in the case of IVP and BVP. In case of four point BVP we
compare the result with other methods. Convergence of these methods is also
established and found to be of second order. We observe that as resolution is
increased to $J=4$ we get the exact values for IVPs and BVPs. For four point
BVPs also at $J=4$, we get highly accurate solutions, e.g., the $L^\infty$
error is of order $10^{-16}$ or $10^{-17}$.
