Necessary conditions for the appearance of noise terms in decomposition solution series

摘要

In this paper, the phenomena of the noise terms that appear in the components of the series solution introduced by Adomian and Rach [1] will be examined extensively. The phenomena is useful in demonstrating a fast convergence of the exact solution. However, the condition set by Adomian and Rach [1] in that these noise terms appear for every nonhomogeneous equation is not always true, and the nonhomogeneity condition is not sufficient. Another necessary condition will be established in this study to ensure the appearance of noise terms in specific cases. Several differential and integral equations will be tested to confirm the newly developed condition.