An approximate solution for the static beam problem and nonlinear integro-differential equations

Authors:
H. Temimi;A. R. Ansari;A. M. Siddiqui
Affiliations:
Department of Mathematics & Natural Sciences, Gulf University for Science & Technology, P.O. Box 7207, Hawally 32093, Kuwait;Department of Mathematics & Natural Sciences, Gulf University for Science & Technology, P.O. Box 7207, Hawally 32093, Kuwait;Department of Mathematics, York Campus, Pennsylvania State University, York, PA 17403, USA
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

We consider a Kirchhoff type nonlinear static beam and an integro-differential convolution type problem, and investigate the effectiveness of the Optimal Homotopy Asymptotic Method (OHAM), in solving nonlinear integro-differential equations. We compare our solutions via the OHAM, with bench mark solutions obtained via a finite element method, to show the accuracy and effectiveness of the OHAM in each of these problems. We show that our solutions are accurate and the OHAM is a stable accurate method for the problems considered.