Table 1 The first four Adomian polynomials and the first four El-Kalla polynomials of the nonlinear term u2
From: An accelerated solution for some classes of nonlinear partial differential equations
Adomian polynomials of u2 | El-Kalla polynomials of u2 |
|---|---|
\(A_{0} = u_{0}^{2}\) | \(\overline{A}_{0} = u_{0}^{2}\) |
\(A_{1} = 2u_{0} u_{1}\) | \(\overline{A}_{1} = 2u_{0} u_{1} + u_{1}^{2}\) |
\(A_{2} = u_{1}^{2} + 2u_{0} u_{2}\) | \(\overline{A}_{2} = 2u_{0} u_{2} + 2u_{1} u_{2} + u_{2}^{2}\) |
\(A_{3} = 2u_{1} u_{2} + 2u_{0} u_{3}\) | \(\overline{A}_{3} = 2u_{0} u_{3} + 2u_{1} u_{3} + 2u_{2} u_{3} + u_{3}^{2}\) |