Convergence of variational iteration method applied to two-point diffusion problems

• A new approach is introduced to construct the variational iteration algorithm-II for diffusion problems.
• The sufficient conditions for convergence of variational iteration method applied to two-point diffusion problems are established.
• An error analysis is given and can be used to estimate the number of steps necessary to obtain the required accuracy in advance.

A new approach is introduced to construct the variational iteration algorithm-II for diffusion problems. Based on this algorithm, the sufficient conditions for convergence of variational iteration method applied to this type of two-point boundary value problems are established. An error analysis is also presented. Several examples are given to illustrate the convergence concept and error estimate.