ABSTRACT
In this chapter, the Legendre spectral collocation method has been applied to solve integro-differential equations. The proposed method is based on the Gauss-Legendre points with the basis functions of Lagrange polynomials. The presented method applied to the integral equation reduces to solve the system of algebraic equations. The Legendre spectral collocation method has been applied to solve the Fredholm integro-differential-difference equation with variable coefficients and mixed conditions in Section 8.2 and the system of integro-differential equations modeling biological species living together in Section 8.3. Also, the numerical results obtained by the Legendre spectral collocation method have been compared with the results obtained by existing methods. Illustrative examples have been discussed to demonstrate the validity and applicability of the presented method.
