In this paper, authors present the reconstruction of variational iteration method (RVIM) in order to obtain the analytical solution of the diffusion equation with a reaction term. This special kind of equation which is used as a mathematical model in geotechnical engineering, fluid mechanics, heat transfer, plasma physics, plasma waves, thermo-elasticity and chemical physics, occurs nonlinearly. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method are discussed. The obtained results reveal that the technique introduced here is very promising and convenient in order to solve nonlinear partial differential equations and nonlinear ordinary differential equations.

reconstruction of variational iteration method (RVIM), diffusion equation, approximate solution.