Solution of a model describing biological species living together using the variational iteration method

In this work, a system of two nonlinear integro-differential equations which arises in biology is considered and the well-known variational iteration method is implemented for finding the solution of this system. This method is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. This technique reduces the volume of calculations by not requiring discretization of the variables, linearization or small perturbations and constructs a sequence which converges to the exact solution rapidly. Also a numerical technique based on the pseudospectral Legendre method is developed to solve the model. Several test problems are given and the results are compared with Adomian decomposition method and the variational iteration technique.