Keywords: Adomian decomposition method Padé approximants Belov–Chaltikian lattice The nonlinear self-dual network equations Solitary solution a b s t r a c t ADM-Padé technique is a combination of Adomian decomposition method (ADM) and Padé approximants. We solve two nonlinear lattice equations using the technique which gives the approximate solution with higher accuracy and faster convergence ...

UNLABELLED This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value proble...

In a previous paper, we showed that genetic programming can be used to evolve approximations to functions which, given certain trade-offs between cost and error, are superior to Padé approximations, which represent a generalization of Taylor series and a powerful technique from numerical analysis. In the present paper, we present an extension to this work which allows existing Padé approximatio...

The learning capability of a network-based computation model named “Algorithmically Transitive Network (ATN)” is extensively studied using symbolic regression problems. To represent a variety of functions uniformly, the ATN’s topological structure is designed in the form of a truncated power series or a Padé approximant. Since the Padé approximation has better convergence properties than the Ta...

Padé approximations are widely used to approximate a dead-time in continuous control systems. It provides a finite-dimensional rational approximation of a dead-time. However, the standard Padé approximation (recommended in many textbooks) with equal numeratorand denominator degree, exhibits a jump at time t=0. This is highly undesirable in simulating dead-times. To avoid this phenomena we shall...

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the Padé technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger’s equation, compacton k(n, n) equation, Zakharov–Kuznetsov Zk(n, n) equation, and KdV and mKdV equations are given to show the effectiveness of the coupled VIM–Laplace–Pa...

Padé approximation is considered from the point of view of robust methods of numerical linear algebra, in particular the singular value decomposition. This leads to an algorithm for practical computation that bypasses most problems of solution of nearly-singular systems and spurious pole-zero pairs caused by rounding errors; a Matlab code is provided. The success of this algorithm suggests that...

In order to reduce the Gibbs phenomenon exhibited by the partial Fourier sums of a periodic function f , defined on [−π, π], discontinuous at 0, Driscoll and Fornberg considered so-called singular Fourier-Padé approximants constructed from the Hermite-Padé approximants of the system of functions (1, g1(z), g2(z)), where g1(z) = log(1 − z) and g2(z) is analytic, such that Re (g2(e)) = f(t). Conv...

Commonly used techniques to study non-perturbative aspects of the strong interactions have a deep connection with rational approximants, and in particular with Padé approximants to meromorphic functions. However, only recently this connection has been acknowledged and efforts at fully exploiting it are only starting. In this article I will briefly review the most prominent techniques used in no...