Abstract:
In this thesis, we have used spectral method for solving the Volterra's di erential
equation. We study the basic theory of this method. The spectral method for the
solution of non-linear Volterra integro-di erential equation is described in details and
is applied. The solutions are compared and the results are plotted graphically. We
analyze Volterra's population model analytically and numerically by using the spectral
method. An analytic approximation was discussed for Volterra's population model and
then the use of the Pade approximants gives a better approximation. We discuss the
rational Chebyshev polynomial for solving the Volterra's population model numerically.
The Laguerre set of polynomials is also used to solve it.
