Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 219, Issue 9, Pages 4423-4433Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2012.10.046
Keywords
Cauchy integral equations; Adomian decomposition method; The method of regularization
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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 phi(epsilon), of the regularized integral equation and prove the convergence of our new combined method. As the regularization parameter epsilon -> 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. (C) 2012 Elsevier Inc. All rights reserved.
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