finite difference discretization for systems of higher ODEs

How can I use finite difference to discretize a system of fourth order differential equations?

y₁⁽⁴⁾=a₁y₁^''+a₂y₂^''+a₃y₃^''+a₄y₁+a₅y₂+a₆y₃+a₇
y₂⁽⁴⁾=b₁y₁^''+b₂y₂^''+b₃y₃^''+b₄y₁+b₅y₂+b₆y₃+b₇
y₃⁽⁴⁾=c₁y₁^''+c₂y₂^''+c₃y₃^''+c₄y₁+c₅y₂+c₆y₃+c₇
where a, b and c terms are constant coefficients