Showing papers in "Applied Mathematics and Computation in 2009"

TL;DR: Results show that the performance of the ABC is better than or similar to those of other population-based algorithms with the advantage of employing fewer control parameters.

TL;DR: A novel version of the method (augmented @e-constraint method - AUGMECON) is proposed that avoids the production of weakly Pareto optimal solutions and accelerates the whole process by avoiding redundant iterations.

TL;DR: The proposed MI-LXPM is a suitably modified and extended version of the real coded genetic algorithm, LXPM, of Deep and Thakur and incorporates a special truncation procedure to handle integer restrictions on decision variables along with a parameter free penalty approach for handling constraints.

TL;DR: A fractional calculus with an integral operator which contains the following family of generalized Mittag-Leffler functions: E"@a","@b^@c^,^@k(z), (@l)"@n being the familiar Pochhammer symbol.

TL;DR: The present study investigates the effects of heat and mass transfer on peristaltic transport in a porous space with compliant walls under long-wavelength and low-Reynolds number approximations.

TL;DR: In order to reduce computational burden and improve the convergence rate of identification algorithms, an auxiliary model based multi-innovation stochastic gradient (AM-MISG) algorithm is derived for the multiple-input single-output systems by means of the auxiliary model identification idea and multi- innovation identification theory.

TL;DR: In this paper, this paper considers the variable-order nonlinear fractional diffusion equation @?u(x,t)@?t=B(X,t)"xR^@a^(^x^,^t^)u( x,t)+f(u,x, t), where xR is a generalized Riesz fractional derivative of variable order.

TL;DR: A modified version of the SIR (Susceptible-Infected-Removed) model is presented and how its parameters are related to network characteristics is explained, and the relations among the model parameters in the several bifurcation conditions allow a network design minimizing viruses risks.

TL;DR: Using the setting of a generalized metric space, a fixed point theorem is proved for one map, and several fixed point theorems are proved for two maps.

TL;DR: First-order consistency, unconditional stability, and first-order convergence of the method are proven using a novel shifted version of the classical Grunwald finite difference approximation for the fractional derivatives.

TL;DR: The closed Newton–Cotes formulae are studied and written as symplectic multilayer structures and trigonometrically-fitted symplectic methods are developed and applied to the well-known radial Schrodinger equation to investigate the efficiency of the proposed method.

TL;DR: The present paper illustrates an iterative numerical method to solve nonlinear equations of the form f(x)=0, especially those containing the partial and non partial involvement of transcendental terms, and demonstrates the higher order convergence of the present method as compared to others without going to the computation of second derivative.

TL;DR: This work investigates the effectiveness of fusing two novel texture features along with intensity in multimodal magnetic resonance (MR) images for pediatric brain tumor segmentation and classification and suggests that the fusion of fractal, fractalwavelet and intensity features in multi-modality MR images offers better tumor segmentsation results when compared to that of just fractal andintensity features in single modality MR pictures.

TL;DR: In this paper, a five-dimensional symmetry algebra consisting of Lie point symmetries is computed for the nonlinear Schrodinger equation, which, together with a reflection invariance, generates two five-parameter solution groups.

TL;DR: A delay-dependent linear matrix inequality (LMI) criterion for existence of the estimator is derived and a numerical simulation is given to show the effectiveness of proposed estimator.

TL;DR: An accurate and efficient Haar wavelet solution of Fisher's equation, a prototypical reaction-diffusion equation, which is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.

TL;DR: This paper newly establish the simulation method based on the operational matrices of the orthogonal functions, and formulate the operational matrix of integration in a unified framework.

TL;DR: The analytical solution has been obtained in the form of temperature from which an axial velocity, stream function and pressure gradient have been derived.

TL;DR: The proposed method for analysing fractional harmonic vibrations using haar wavelets for the solution of fractional integral equations and its efficiency is demonstrated.

TL;DR: This paper considers the so-called boundary immobilization method for four benchmark melting problems, in tandem with three finite-difference discretization schemes, and demonstrates a combined analytical and numerical approach that eliminates completely the ad hoc treatment of the starting solution and is numerically second-order accurate in both time and space.

TL;DR: A family of trigonometrically fitted partitioned Runge–Kutta symplectic methods of fourth order with six stages considering the solution of the one-dimensional time independent Schrodinger equation is presented.

TL;DR: The present framework offers a computationally easier approach to compute the transformed function for all forms of nonlinearity, which gives the technique much wider applicability.

TL;DR: Improved conditions for the global asymptotic stability of a class of neural networks with interval time-varying delays are provided by a piecewise delay method.

TL;DR: The validity and reliability of the so-called (G′/G)-expansion method is tested by applying it to two nonlinear evolutionary equations and it is observed that the previously known solutions can be recovered.

TL;DR: The existence of a positive solution to a singular boundary value problem of nonlinear fractional differential equation of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone is established.

TL;DR: A family of eighth-order iterative methods with four evaluations for the solution of nonlinear equations is presented and agrees with the conjecture of Kung-Traub for the case n=4.

TL;DR: By solving the matrix equation, Legendre coefficients and polynomial approach are obtained by solving high-order Linear Fredholm integro-differential equations under the mixed conditions in terms of Legendre polynomials.

TL;DR: In this article, the higher-order nonlinear Schrodinger equation is reduced to a nonlinear ordinary differential equation (ODE) by using a simple transformation, various solutions of the nonlinear ODE are obtained by the ( G ′/G )-expansion method proposed recently.

TL;DR: In this paper, a new fourth-order method for finding multiple roots of nonlinear equations is presented, which requires one evaluation of the function and two of its first derivative per iteration.

TL;DR: The SIR and SIS epidemic models in biology are solved by means of an analytic technique for nonlinear problems, namely the homotopy analysis method (HAM), and a one-parameter family of explicit series solutions are obtained.