Nonlinear Flow Phenomena and Homotopy Analysis Fluid Flow and Heat Transfer - Vajravelu, Kuppalapalle; Van Gorder, Robert A.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012)
Since most of the problems arising in science and engineering are nonlinear, they are inherently difficult to solve. Traditional analytical approximations are valid only for weakly nonlinear problems, and often fail when used for problems with strong nonlinearity. “Nonlinear Flow Phenomena and Homotopy Analysis: Fluid Flow and Heat Transfer” presents the current theoretical developments of the analytical method of homotopy analysis. This book not only addresses the theoretical framework for the method, but also gives a number of examples of nonlinear problems that have been solved by means of the homotopy analysis method. The particular focus lies on fluid flow problems governed by nonlinear differential equations. This book is intended for researchers in applied mathematics, physics, mechanics and engineering. Both Kuppalapalle Vajravelu and Robert A. Van Gorder work at the University of Central Florida, USA.
Part I: Theoretical Considerations.- Principles of the Homotopy Analysis Method -- Methods for the Control of Convergence in Obtained Solutions -- Additional Techniques. Part II: Applications to Physical Problems -- Application of the Homotopy Analysis Method to Fluid Flow Problems -- Application of the Homotopy Analysis Method to Heat Transfer Problems -- Application of the Homotopy Analysis Method to More Advanced Problems.
Keywords: Computer mathematics; Fluid mechanics; Mathematical physics; Differential equations; Partial differential equations; Computational Mathematics and Numerical Analysis; Engineering Fluid Dynamics; Theoretical, Mathematical and Computational Physics; Computational Science and Engineering; Ordinary Differential Equations; Partial Differential Equations