New approach for convergence of the series solution to a class of nonlinear Hammerstein integral equations.

摘要

The proof of convergence of the series solution to a class of nonlinear two-dimensional Hammerstein integral equation (NTHIE), including the necessary and su￠ cient conditions that guarantee a unique solution, is introduced. Adomian Decomposition Method (ADM) and Homotopy Analysis Method (HAM) are used to solve the NTHIE. It was found that, when using the traditional Adomian polynomials (4), ADM and HAM are exactly the same. But, when using the proposed accelerated Adomian polynomials formula (5), ADM converges faster than HAM. The proposed accelerated Adomian polynomials formula is used directly to prove the convergence of the series solution. Convergence approach is reliable enough to estimate the maximum absolute truncated error.