The method of step by step inversion for numerical solution of the biharmonic equation (Q1921810)

For the boundary value problem \[ Lu \equiv (k(x)u''(x))'' =f(x); \quad u(0)=u'(0) = u'(1)=u(1)=0 \] a difference approximation which follows from the factorization of the differential operator \(L\) is derived. The corresponding system of linear equations is solved using a factorization method. This method requires \(N\) divisions, \(3N\) multiplications and \(15N\) additions.