[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 …

[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 …

[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 …

[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 …

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 …

Adomian decomposition method for a reliable treatment of the Bratu-type equations

AM Wazwaz - Applied Mathematics and Computation, 2005‏ - Elsevier
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 …

Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines

G Fabiani, F Calabrò, L Russo, C Siettos - Journal of Scientific Computing, 2021‏ - Springer
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 …

Orthogonal rational functions on a semi-infinite interval

JP Boyd - Journal of Computational Physics, 1987‏ - Elsevier
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 …

New directions in solitons and nonlinear periodic waves: Polycnoidal waves, imbricated solitons, weakly nonlocal solitary waves, and numerical boundary value …

JP Boyd - Advances in applied mechanics, 1989‏ - Elsevier
Publisher Summary This chapter describes polycnoidal waves, periodic waves as exact
imbricate series of solitons, and numerical boundary value algorithms for direct computation …

Thermo-electro-hydrodynamic model for electrospinning process

YQ Wan, Q Guo, N Pan - International Journal of Nonlinear Sciences …, 2004‏ - degruyter.com
Ultra-fine polymer fibers, obtained by electrospinning, have a wide range of potential
applications such as fluid filtration, biomedicine, catalyst supports, drug delivery, tissue …