In this paper, an
algorithm based on integral collocation and variational iteration method for
solving integro-differential equations is presented. In the rst instance,
integro-differential equations are reduced to a system of integral equations
after which we replaced all the derivatives in the new system of integral
equations with their equivalent new derivatives. These new derivatives were
obtained by approximating the nth order derivative with truncated Chebyshev
series and then integrated n-times to obtain expressions for lower-order
derivatives and the function itself. After the second iteration, the residual
equation is formed which is collocated at the chosen collocation points and
extra n equations are also obtained from the boundary conditions. Computational
results are given for test examples to demonstrate the effectiveness,
reliability, applicability and efficiency of the new method. It is shown that
the solutions obtained from the method have very high degree of accuracy.
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