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[ספר][B] Homotopy analysis method in nonlinear differential equations
S Liao - 2012 - Springer
It is well-known that perturbation and asymptotic approximations of nonlinear problems often
break down as nonlinearity becomes strong. Therefore, they are only valid for weakly …
break down as nonlinearity becomes strong. Therefore, they are only valid for weakly …
[ספר][B] Chebyshev and Fourier spectral methods
JP Boyd - 2001 - books.google.com
Completely revised text focuses on use of spectral methods to solve boundary value,
eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational …
eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational …
[ספר][B] Spectral methods for incompressible viscous flow
R Peyret - 2002 - Springer
The objective of this book is to provide a comprehensive discussion of Fourier and
Chebyshev spectral methods for the computation of incom pressible viscous flows, based on …
Chebyshev spectral methods for the computation of incom pressible viscous flows, based on …
[ספר][B] Advances in the homotopy analysis method
S Liao - 2013 - books.google.com
Unlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of
small/large physical parameters. Besides, it provides great freedom to choose equation type …
small/large physical parameters. Besides, it provides great freedom to choose equation type …
A general approach to obtain series solutions of nonlinear differential equations
S Liao, Y Tan - Studies in Applied Mathematics, 2007 - Wiley Online Library
Based on homotopy, which is a basic concept in topology, a general analytic method
(namely the homotopy analysis method) is proposed to obtain series solutions of nonlinear …
(namely the homotopy analysis method) is proposed to obtain series solutions of nonlinear …
Adomian decomposition method for a reliable treatment of the Bratu-type equations
In this paper, we present a framework to determine exact solutions of Bratu-type equations.
The algorithm rests mainly on the Adomian decomposition method. The proposed scheme is …
The algorithm rests mainly on the Adomian decomposition method. The proposed scheme is …
Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines
We address a new numerical method based on a class of machine learning methods, the so-
called Extreme Learning Machines (ELM) with both sigmoidal and radial-basis functions, for …
called Extreme Learning Machines (ELM) with both sigmoidal and radial-basis functions, for …
Orthogonal rational functions on a semi-infinite interval
By applying a map** to the Chebyshev polynomials, we define a new spectral basis: the
“rational Chebyshev functions on the semi-infinite interval,” denoted by TL n (y). Continuing …
“rational Chebyshev functions on the semi-infinite interval,” denoted by TL n (y). Continuing …
New directions in solitons and nonlinear periodic waves: Polycnoidal waves, imbricated solitons, weakly nonlocal solitary waves, and numerical boundary value …
Publisher Summary This chapter describes polycnoidal waves, periodic waves as exact
imbricate series of solitons, and numerical boundary value algorithms for direct computation …
imbricate series of solitons, and numerical boundary value algorithms for direct computation …
Thermo-electro-hydrodynamic model for electrospinning process
Ultra-fine polymer fibers, obtained by electrospinning, have a wide range of potential
applications such as fluid filtration, biomedicine, catalyst supports, drug delivery, tissue …
applications such as fluid filtration, biomedicine, catalyst supports, drug delivery, tissue …