Search

The objective of present study is to investigate the two-dimensional magnetohydrodynamic (MHD) flow of a viscous fluid over a constant wedge immersed in a porous medium with velocity slip condition. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with co-ordinate distance along the boundary. Similarity transformations are used to convert the governing nonlinear boundary layer equations into a third order Falkner–Skan equation. This equation is solved analytically by using a novel analytical method called DTM-Padé technique which is a combination of the differential transformation method and the Padé approximation. This method is applied to give solutions of equation with boundary condition at infinity. Graphical results are presented to investigate the effects of the velocity slip parameter, Hartmann number, permeability, suction/injection parameter and nonlinear pressure gradient on the flow-field. Further, the results of the present analysis have been compared with the corresponding results available in literature. Our results have been found in excellent agreement. [ABSTRACT FROM AUTHOR]

We obtain highly accurate solutions to the Thomas–Fermi equations for atoms and atoms in very strong magnetic fields. We apply the Padé–Hankel method, numerical integration, power series with Padé and Hermite–Padé approximants and Chebyshev polynomials. Both the slope at origin and the location of the right boundary in the magnetic-field case are given with unprecedented accuracy. [ABSTRACT FROM AUTHOR]

Abstract: The numerical simulation of colliding solitary waves with compact support arising from the Rosenau–Hyman equation requires the addition of artificial dissipation for stability in the majority of methods. The price to pay is the appearance of trailing tails, amplitude damping, and delays as the solution evolves. These undesirable effects can be corrected by properly counterbalancing two sources of artificial dissipation; this procedure is designed by using the slow time evolution of the parameters of the solitary waves under the presence of the dissipation determined by means of adiabatic perturbation methods. The validity of the tail removal methodology is demonstrated on a Padé numerical scheme. The tails are completely removed leaving only a small compact ripple at the original position of their front, and the numerical stability of the scheme under compacton collisions is preserved, as shown by extensive numerical experiments for several values of n. [Copyright &y& Elsevier]

Abstract: We show that a simple and straightforward rational approximation to the Thomas–Fermi equation provides the slope at origin with unprecedented accuracy and that Padé approximants of relatively low order are far more accurate than more elaborate approaches proposed recently by other authors. We consider both the Thomas–Fermi equation for isolated atoms and for atoms in strong magnetic fields. [Copyright &y& Elsevier]

Abstract: The Adomian decomposition method and the asymptotic decomposition method give the near-field approximate solution and far-field approximate solution, respectively, for linear and nonlinear differential equations. The Padé approximants give solution continuation of series solutions, but the continuation is usually effective only on some finite domain, and it can not always give the asymptotic behavior as the independent variables approach infinity. We investigate the global approximate solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from the asymptotic decomposition method for linear and nonlinear differential equations. For several examples we find that there exists an overlap between the near-field approximation and the far-field approximation, so we can match them to obtain a global approximate solution. For other nonlinear examples where the series solution from the Adomian decomposition method has a finite convergent domain, we can match the Padé approximant of the near-field approximation with the far-field approximation to obtain a global approximate solution representing the true, entire solution over an infinite domain. [Copyright &y& Elsevier]

Abstract: Using Padé approximation to the exponential function, we obtain new identities involving values of the Rieman zeta function at integers. Applications to series associated with zeta numbers are proved. In particular, expansion of ζ(3) (resp. ζ(5)) in terms of ζ(4j +2) (resp. ζ(4j)) are proved. [Copyright &y& Elsevier]

Abstract: 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 rate than using ADM alone. Bell-shaped solitary solution of Belov–Chaltikian (BC) lattice and kink-shaped solitary solution of the nonlinear self-dual network equations (SDNEs) are presented. Comparisons are made between approximate solutions and exact solutions to illustrate the validity and the great potential of the technique. [Copyright &y& Elsevier]

Abstract: The variational iteration method is applied for a reliable treatment of two forms of the third order nonlinear Blasius equation which comes from boundary layer equations. The study shows that the series solution is obtained without restrictions on the nonlinearity behavior. The obtained series solution is combined with the diagonal Padé approximants to handle the boundary condition at infinity for only one of these forms. [Copyright &y& Elsevier]

Abstract: In this paper, an algorithm based on Adomian’s decomposition method is developed to approximate the solution of the ratio-dependent predator–prey system with constant effort harvesting. The convergence of the decomposition series is enhanced using Padé approximation technique. The qualitative analysis of the model reveals that constant effort prey harvesting may contribute to mutual extinction as a possible outcome of predator–prey interaction. Some plots of the population of predator and prey versus time are presented to illustrate the performance and the accuracy of the algorithm. The decomposition method has the advantage of being more concise for numerical purposes. [Copyright &y& Elsevier]

Abstract: In this paper, we present a reliable combination of Adomian decomposition algorithm and Padé approximants to investigate the Flierl–Petviashivili (FP) equation and its variants. The approach introduces an alternative framework designed to overcome the difficulty of the singular point at x =0. We also investigate two generalized variants of the FP equation. The proposed framework reveals quite a number of remarkable features of the combination of the two algorithms. [Copyright &y& Elsevier]

Abstract: In this article, we implement a relatively new analytical technique, the Adomian decomposition method, for solving fractional Riccati differential equations. The fractional derivatives are described in the Caputo sense. In this scheme, the solution takes the form of a convergent series with easily computable components. The diagonal Padé approximants are effectively used in the analysis to capture the essential behavior of the solution. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the method. [Copyright &y& Elsevier]

Abstract: In this study we present iterative regularization methods using rational approximations, in particular, Padé approximants, which work well for ill-posed problems. We prove that the (k, j)-Padé method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Padé method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Böckmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385–397] where this method was treated to solve ill-conditioned equation systems. [Copyright &y& Elsevier]

Abstract: The modified decomposition method is applied for analytic treatment of nonlinear differential equations that appear on boundary layers in fluid mechanics. The modified method accelerates the rapid convergence of the series solution, dramatically reduces the size of work. The obtained series solution is combined with the diagonal Padé approximants to handle the boundary condition at infinity. [Copyright &y& Elsevier]

Abstract: In this study we present iterative methods using rational approximations, e.g., Padé approximants, which work very well for strongly ill-conditioned systems. In principle all methods of the family are convergent. One type of those methods has the advantage that their convergence behavior is very fast without additional a-priori information on the optimal relaxation parameter. [Copyright &y& Elsevier]

In this paper, we propose a new approach for solving boundary value problems a differential equation with retarded argument:x″(t)+a(t)x(t−τ(t))=f(t),x(t)=ϕ(t)(λ0⩽t⩽0), x(T)=xT ,where 0⩽t⩽T and a(t), f(t), τ(t)⩾0(0⩽t⩽T) and ϕ(t)(λ0⩽t⩽0) are known continuous functions. A differential equation with retarded argument is computed by converting the obtained series solution into padé series. First we calculate power series of the given equation system then transform it into padé (approximants) series form, which give an arbitrary order for solving differential equation numerically. [Copyright &y& Elsevier]

In this paper, we suggested an successive approximation method and Pade´ approximants method for the solution of the non-linear differential equation. First we calculate power series of the given equation system then transform it into Pade´ (approximants) series form, which give an arbitrary order for solving differential equation numerically. We compare our results with the result obtained by successive method for the non-linear equation. [Copyright &y& Elsevier]

The aim of this paper is to present an efficient numerical procedure for solving boundary value problems for a differential equation with retarded argument:x′′(t)+a(t)x(t−τ(t))=f(t),x(t)=ϕ(t) (λ0⩽t⩽0), x(T)=xT,where 0⩽t⩽T and a(t),f(t),τ(t)⩾0 (0⩽t⩽T) and ϕ(t) (λ0⩽t⩽0) are known continuous functions. A differential equation with retarded argument is computed by converting the obtained series solution into Pade´ (approximants) series. First we calculate power series of the given equation system then transform it into Pade´ (approximants) series form, which give an arbitrary order for solving differential equation numerically. [Copyright &y& Elsevier]

The aim of this paper is to present an efficient numerical procedure for solving boundary value problems for a differential equation with retarded argument:x″(t)+a(t)x(t−τ(t))=f(t)x(t)=ϕ(t) (λ0⩽t⩽0), x(T)=xT,where 0⩽t⩽T and a(t),f(t),τ(t)⩾0 (0⩽t⩽T) and ϕ(t) (λ0⩽t⩽0) are known continuous functions. A differential equation with retarded argument is computed by converting the obtained series solution into Pade´ (approximants) series. First we calculate power series of the given equation system then transform it into Pade´ (approximants) series form, which give an arbitrary order for solving differential equation numerically. [Copyright &y& Elsevier]