tailieunhanh - báo cáo hóa học: " An improved spectral homotopy analysis method for solving boundary layer problems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: An improved spectral homotopy analysis method for solving boundary layer problems | Motsa et al. Boundary Value Problems 2011 2011 3 http content 2011 1 3 0 Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access An improved spectral homotopy analysis method for solving boundary layer problems Sandile Sydney Motsa1 Gerald T Marewo1 Precious Sibanda2 and Stanford Shateyi3 Correspondence Stanford. shateyi@ department of Mathematics University of Venda Private Bag X5050 Thohoyandou 0950 SoUth Africa Full list of author information is available at the end of the article SpringerOpen0 Abstract This article presents an improved spectral-homotopy analysis method ISHAM for solving nonlinear differential equations. The implementation of this new technique is shown by solving the Falkner-Skan and magnetohydrodynamic boundary layer problems. The results obtained are compared to numerical solutions in the literature and MATLAB s bvp4c solver. The results show that the ISHAM converges faster and gives accurate results. Keywords Falkner-Skan flow MHD flow improved spectral-homotopy analysis method Introduction Boundary layer flow problems have wide applications in fluid mechanics. In this article we propose an improved spectral-homotopy analysis method ISHAM for solving general boundary layer problems. Three boundary layer problems are considered and solved in this study using the novel technique. The first problem considered is the classical two-point nonlinear boundary value Blasius problem which models viscous fluid flow over a semi-infinite flat plate. Although solutions for this problem had been obtained as far back as 1908 by Blasius 1 the problem is still of great interest to many researchers as can be seen from the several recent studies 2-5 . The second problem considered in this article is the third-order nonlinear Falkner-Skan equation. The Falkner-Skan boundary layer equation has been studied by several researchers from as early as 1931 6 . More recent studies of the solutions of the The .