The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional differential equations
In this paper, we present the Adomian decomposition method and its modifications combined with convergence acceleration techniques, such as the diagonal Pad approximants and the iterated Shanks transforms, to solve nonlinear fractional ordinary differential equations. Two nonlinear numeric examples demonstrate that either the diagonal Pad approximants or the iterated Shanks transforms can efficiently extend the effective convergence region of the decomposition series solution.
adomian decomposition method fractional differential equations fractional calculus adomian polynomials power series