The decomposition method applied to systems of linear Volterra integral equations of the first kind

The purpose of this paper is to solve systems of linear Volterra integral equations of the first kind by the Adomian decomposition method (ADM). An elegant and reliable technique is outlined to find canonical form of ADM.

The approximate solution of systems of linear Volterra integral equations is calculated in the form of series with easily computable components. In this work, some methods based on substitution techniques are presented to permit the application of ADM to systems of integral equations of the first kind.

The approach developed in this work is valuable as a tool for scientists and applied mathematicians. It provides immediate and visible symbolic terms of analytical solution as well as its numerical approximate solution to systems of integral equations of the first kind, without linearization or discretization. The presented technique has many advantages over the traditional methods because it takes into account some systems of integral equations of first kind where the kernels present some singularities.

A reliable method for obtaining approximate solutions of linear systems of integral equations of the first kind using the ADM which avoids the tedious work needed by traditional techniques has been developed.

The research provides a new efficient method for solving systems of integral equations of first kind using ADM. The convergence result is investigated also and some numerical examples are given to illustrate the importance of the analysis presented.

The technique is both innovative and efficient, and an original approach for solving any kind of systems of linear Volterra integral equations of the first kind.