On error of certain projection-grid methods for an ordinary differential equation of 4-th order with non-smooth data (Q1909826)

The boundary value problem for the differential equation \((a_2 u'')''- (a_1 u')'+ a_0 u= f\), \(x\in \Omega= (0, X)\), \(u(0)= u'(0)= u(X)= u'(X)= 0\) is studied. The coefficients are measurable and bounded, \(f\in L_p(\Omega)\) or \(f\) is a generalized function. A projective grid method, which uses generalized piecewise ``cubic'' Hermitian splines, is studied. Bounds of the error in the norm of \(W^2_2(\Omega)\) in dependence of properties of \(a_1\), \(a_2\) and \(f\) are obtained.