A new efficient multi-parametric homotopy approach for two-dimensional Fredholm integral equations of the second kind

Yıl 2015, Cilt: 44 Sayı: 1, 93 - 99, 01.02.2015

Y. Khan M. Fardi

Öz

In this paper, a new multi-parametric homotopy approach is proposed to find
the approximate solution of linear and non-linear two-dimensional Fredholm
integral equations of the second kind. In this framework, convergence of the
proposed approach for these types of equations is investigated. This homotopy contain two auxiliary parameters that provide a simple way of controlling
the convergence region of series solution. The results of present method are
compared with Adomian decomposition method (ADM) results which provide
confirmation for the validity of proposed approach. Two examples are presented
to illustrate the accuracy and effectiveness of the proposed approach.

Anahtar Kelimeler

multi-parametric, convergence-control, Adomian decomposition method (ADM), Fredholm integral equation, averaged residual error (ARE)

Kaynakça

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