A series solution for nonlinear differential equations using delta operators

In this paper, we shall generalize our previous results [1] to the case of series expansion in powers of several polynomials. For this, we shall extend the ideas of delta operators and their basic polynomial sequences, introduced in conjunction with the algebra (over a field of characteristic zero) of all polynomials in one variable [2] to the algebra (over a field of characteristic zero) of all polynomials in n indeterminates, We apply this technique to derive the formal power series expansion of the input-output map describing a nonlinear system with polynomial inputs.