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In this paper, the homoto pyanalysis method (HAM) is presented to solve some of engineering problems. The homotopy analysis method is applied in obtaining exact solutions for equations of the type Δ2=b(x,y) and  Δ2u=b(x,y,u) on an elliptical domain. Exact solutions are presented for several examples involving to demon strate the applic ability and efficiency of HAM.

journal of applied mathematics and physics

Homotopy Analysis Method for Equations of the Type &amp;amp;Delta;&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;=b(x,y) and &amp;amp;Delta;&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;u=b(x,y,u)