In this work, we have carefully developed a new modification
of Adomian decomposition method based on the Taylor
expansion of the components apart from the zeroth term for
Volterra integral equations. The new technology overcomes
such obstacles as the complicated integrals and the impossible
integrals analytically, which arise from either SADM or
MADM2. If the exact solution exists in the zeroth component,
MADM1 needs extensive workload for the suitable choice of