Showing papers in "Applied Mathematics and Computation in 2004"

TL;DR: A powerful, easy-to-use analytic tool for nonlinear problems in general, namely the homotopy analysis method, is further improved and systematically described through a typical nonlinear problem, i.e. the algebraically decaying viscous boundary layer flow due to a moving sheet.

TL;DR: The homotopy perturbation method is applied to the nonlinear oscillators with discontinuities and only one iteration leads to high accuracy of the solutions.

TL;DR: Comparison of homotopy perturbation method (HPM) and Homotopy analysis method is made, revealing that the former is more powerful than the later.

TL;DR: This paper presents a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection, Wiener-Hopf equations, updating the solution, auxiliary principle, inertial proximal, penalty function, dynamical system and well-posedness.

TL;DR: The tanh method is employed for traveling wave solutions of nonlinear equations and the study is extended to equations that do not have tanh polynomial solutions.

TL;DR: Three-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time and exact solutions of linear and non-linear systems of partial differential equations have been investigated.

TL;DR: Some inequalities are presented here for differentiable convex mappings, using Hermite-Hadamard's integral inequality holding for convex functions, and some error estimates for the midpoint formula are obtained.

TL;DR: The analytical questions of existence and uniqueness of solutions are discussed, and how the solutions depend on the given data are investigated, and convergent and stable numerical methods are proposed for such initial value problems.

TL;DR: The effect of a magnetic field on peristaltic transport of blood in a non-uniform two-dimensional channels has been investigated under zero Reynolds number with long wavelength approximation and it is found that the pressure rise decreases as the couple-stress fluid parameter @c increases and increases as the Hartmann number M increases.

TL;DR: Sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a Hopfield-type neural network with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time.

TL;DR: In the paper, an heuristical example is given to illustrate the basic idea of the homotopy perturbation method, which has made all that is necessary simple, andall that is complex unnecessary.

TL;DR: This study investigates the dynamics of a nonlinear discrete-time duopoly game, where the players have heterogeneous expectations and demonstrates that as some parameters of the game are varied, the stability of Nash equilibrium is lost through period doubling bifurcation.

TL;DR: This study proposes ratio estimators by adapting the estimators' type of Ray and Singh to traditional and the other ratio-type estimators in simple random sampling in literature and finds the conditions, which make each proposed estimator more efficient than the others.

TL;DR: An alternative (t,n) multi-secret sharing based on Shamir's secret sharing is proposed, which shall use (n+p-t+1) or (n-1) public values, 2-t-1 or 2-p-1 storages, and employ the Lagrange interpolation polynomial to share p secrets.

TL;DR: Numerical algorithms for solving fuzzy system of linear equations (FSLE) based on the iterative Jacobi and Gauss Sidel methods in detail are considered and there are followed by convergence theorems.

TL;DR: A framework to obtain exact solutions to Fisher's equation and to a nonlinear diffusion equation of the Fisher type by employing Adomian decomposition method is developed.

TL;DR: The main goal of this paper is to verify the viability of using genetic algorithm to solve the OPF problem simultaneously composed by the load flow and the economic dispatch problem.

TL;DR: An analysis of the steady MHD asymmetric flow of an electrically conducting fluid past a semi-infinite stationary plate is considered in the presence of radiation and numerical solutions for the temperature field have been derived and the effect of the radiation parameter is discussed.

TL;DR: An extension of the beta function by introducing an extra parameter, which proved to be useful earlier, is applied here to extend the hypergeometric and confluenthypergeometric functions.

TL;DR: A modification of the Newton method, based on quadrature formulas of order at least one, is extended, which produces iterative methods with order of convergence three that may be more efficient then other third-order methods as they do not require the use of the second-order Frechet derivative.

TL;DR: The approximate solutions for the Burger's-Huxley and Burger’s-Fisher equations are obtained by using the Adomian decomposition method and only few terms of the expansion are required to obtain the approximate solution.

TL;DR: Numerical solution of linear differential-algebraic equations (DAEs) is considered by differential transform method and solutions have been compared very well with those obtained by exact solutions.

TL;DR: A sine-cosine method is used to demonstrate this work and establishes compact and noncompact solutions for nonlinear dispersive equations.

TL;DR: Various numerical techniques will be developed and compared for solving the one-dimensional advection-diffusion equation with constant coefficient using the modified equivalent partial differential equation approach, developed from the 1974 work of Warming and Hyett.

TL;DR: Results show that the method converges rapidly and approximates the exact solution very accurately using only few iterates of the recursive scheme.

TL;DR: The existence of a positive solution to a singular coupled system of nonlinear fractional differential equations based on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone is established.

TL;DR: The proposed algorithm is based mainly on applying the Adomian decomposition method to the transformation of the Blasius equation and demonstrates reliability and efficiency of the proposed algorithm.

TL;DR: Adomian decomposition method is used, which is a well-known method for solving functional equations now-a-days, to solve systems of differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one.

TL;DR: The suggested method, which is called multistage Adomian's decomposition method (MADM), can be considered as an extension of the ADM which is very efficient in solving a variety of differential and algebraic equations.

TL;DR: The fractional calculus approach is taken into account in the constitutive relationship of viscoelastic fluid model and some interesting flows caused by certain special oscillations are established.