The central difference approximation of \(d^{4} W / d x^{4}-\beta^{4} W=0\) at grid point \(i\) with step size \(h\) is

a. \(W_{i+2}-4 W_{i+1}+\left(6-h^{4} \beta^{4}\right) W_{i}-4 W_{i-1}+W_{i-2}=0\)

b. \(W_{i+2}-6 W_{i+1}+\left(6-h^{4} \beta^{4}\right) W_{i}-6 W_{i-1}+W_{i-2}=0\)

c. \(W_{i+3}-4 W_{i+1}+\left(6-h^{4} \beta^{4}\right) W_{i}-4 W_{i-1}+W_{i-3}=0\)