  We present a new algorithm by which the Adomian polynomials can be determined
for scalar-valued nonlinear polynomial functional in a Hilbert space. This
algorithm calculates the Adomian polynomials without the complicated operations
such as parametrization, expansion, regrouping, differentiation, etc. The
algorithm involves only some matrix operations. Because of the simplicity in
the mathematical operations, the new algorithm is faster and more efficient
than the other algorithms previously reported in the literature. We also
implement the algorithm in the MATHEMATICA code. The computing speed and
efficiency of the new algorithm are compared with some other algorithms in the
one-dimensional case.
