Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4629207 | Applied Mathematics and Computation | 2013 | 11 Pages |
Abstract
A new approach is presented to resolve Cauchy integral equations of the first kind in the general case by first considering a regularized integral equation and then transforming it into a canonical form suitable for applying the Adomian decomposition method (ADM). We obtain a decomposition solution φϵφϵ of the regularized integral equation and prove the convergence of our new combined method. As the regularization parameter ϵ→1ϵ→1, the obtained solution is shown to be a sufficiently good approximate solution for the particular Cauchy integral equation. The proposed method has been tested for a variety of Cauchy integral equations, which are particularly important in engineering applications, e.g. airfoil design, etc.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Lazhar Bougoffa, Abdelaziz Mennouni, Randolph C. Rach,