On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: A general approach
Abbreviated Journal Title
Commun. Nonlinear Sci. Numer. Simul.
Homotopy Analysis Method; Nonlinear differential equations; Series; solutions; Perturbation methods; ANALYTIC SOLUTION; KDV EQUATION; SOLITON-SOLUTIONS; SERIES SOLUTIONS; GRADE FLUID; FLOW; SOLVE; SYSTEM; FILM; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical
The Homotopy Analysis Method of Liao [Liao SJ. Beyond perturbation: introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall/CRC Press; 20031 has proven useful in obtaining analytical solutions to various nonlinear differential equations. In this method, one has great freedom to select auxiliary functions, operators, and parameters in order to ensure the convergence of the approximate solutions and to increase both the rate and region of convergence. We discuss in this paper the selection of the initial approximation, auxiliary linear operator, auxiliary function, and convergence control parameter in the application of the Homotopy Analysis Method, in a fairly general setting. Further, we discuss various convergence requirements on solutions. (C) 2009 Elsevier B.V. All rights reserved.
Communications in Nonlinear Science and Numerical Simulation
"On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: A general approach" (2009). Faculty Bibliography 2000s. 2252.