D. Altıntan, Ö. Uğur, Variational Iteration Method for Sturm-Liouville Differential Equations, Computers and Mathematics with Applications, 58(2), pp. 322-328, (July 2009).
In this article, He’s variational iteration method is applied to linear Sturm–Liouville eigenvalue and boundary value problems, including the harmonic oscillator. In this method, solutions of the problems are approximated by a set of functions that may include possible constants to be determined from the boundary conditions. By computing variations, the Lagrange multipliers are derived and the generalised expressions of variational iterations are constructed. Numerical results show that the method is simple, however powerful and effective.
Keywords: variational iteration method, Sturm-Liouville equations, eigenvalue problems, boundary value problems, computing variations, Lagrange multipliers