Collocation for high order differential equations with two-points Hermite boundary conditions

For the numerical solution of high even order differential equations with two-points Hermite boundary conditions a general collocation method is derived and studied. Computation of the integrals which appear in the coefficients are generated by a recurrence formula and no integrals are involved in the calculation. An application to the solution of the beam problem is given. Numerical experiments provide favorable comparisons with other existing methods.