Legendre spectral collocation method for the solution of the model describing biological species living together

In this article, numerical techniques have been developed to solve a system of two nonlinear integro-differential equations which arises in biological model. This model has been solved by Legendre spectral collocation method and Bernstein polynomials. The present methods reduce this model to a system of nonlinear algebraic equations and again this algebraic system has been solved numerically by Newton’s method. Also the results obtained by present methods have been compared with that of by some existing methods available in literature. Some illustrative examples have been discussed to show the applicability and accuracy of the present methods.