Showing papers in "Applied Mathematics and Computation in 2007"

TL;DR: The impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented and the proposed algorithm can find better solutions when compared to HS and other heuristic or deterministic methods.

TL;DR: A new generalized Taylor’s formula of the kind f ( x) = ∑ j = 0 n a j ( α ) ( x - a ) j α + R n α ( x ) , where a j ∈ R, x > a, 0 α ⩽ 1, is established.

TL;DR: The stated results show that the proposed method could point out the ability of design of a new intelligent assistance diagnosis system.

TL;DR: In this article, a hybrid algorithm combining particle swarm optimization (PSO) algorithm with back-propagation (BP) algorithm, also referred to as PSO-BP algorithm, is proposed to train the weights of feedforward neural network (FNN), the hybrid algorithm can make use of not only strong global searching ability of the PSOA, but also strong local searching capability of the BP algorithm.

TL;DR: This paper further discusses the properties of three kinds of fractional derivatives: the Grunwald-Letnikov derivative, the Riemann-Liouville derivative and the Caputo derivative, and compares them with the classical derivative.

TL;DR: Using mathematical induction, it is proved that the IDM is unconditionally stable and convergent, but the EDM is conditionally stable and Convergent.

TL;DR: A differential evolution approach based on a co-evolution mechanism, named CDE, is proposed to solve the constrained problems and both the satisfactory solutions and suitable penalty factors can be obtained simultaneously.

TL;DR: A hybrid PSO (HPSO) with a feasibility-based rule is proposed to solve constrained optimization problems and it is shown that the rule requires no additional parameters and can guide the swarm to the feasible region quickly.

TL;DR: This paper presents a numerical analysis for flow and heat transfer in a viscous fluid over a nonlinear stretching sheet by employing a novel numerical procedure that converts governing partial differential equations into highly nonlinear ordinary differential equations by a similarity transformation.

TL;DR: A new classification method, referred to as move median centers (MMC) hypersphere classifier, for the leaf database based on digital morphological feature is proposed, which is more robust than the one based on contour features since those significant curvature points are hard to find.

TL;DR: The comparative study shows that Laplace crossover (LX) performs quite well and one of the genetic algorithms defined (Lx–MPTM) outperforms other genetic algorithms.

TL;DR: The third or fifth order of convergence of these variants of Newton's method for dimension one, and the second or third order in several variables, depending on the behaviour of the second derivative are proved.

TL;DR: The results show that the RCGA using the proposed power mutation, when used in conjunction with the earlier defined Laplace crossover, outperforms all other GAs considered in this study.

TL;DR: A simple pheromone-guided mechanism to improve the performance of PSO method for optimization of multimodal continuous functions is explored and numerical results comparisons with different metaheuristics demonstrate the effectiveness and efficiency of the proposed PSACO method.

TL;DR: A modified particle swarm optimization algorithm with dynamic adaptation that remarkably improves the ability of PSO to jump out of the local optima and significantly enhance the convergence precision.

TL;DR: The extended tanh method is used to derive new solitons solutions for several forms of the fifth-order nonlinear KdV equation, and Entirely new bell shapedsolitons are determined.

TL;DR: In this paper, an improved particle swarm optimization (IPSO) algorithm is proposed, where a population of points sampled randomly from the feasible space is partitioned into several sub-swarms, each of which is made to evolve based on PSO algorithm.

TL;DR: The extended tanh method with a computerized symbolic computation is used for constructing the travelling wave solutions of coupled nonlinear equations arising in physics and the obtained solutions include solitons, kinks and plane periodic solutions.

TL;DR: This paper compared HBMK-means with other heuristics algorithm in clustering, such as GA, SA, TS, and ACO, by implementing them on several well-known datasets and shows that the proposed algorithm works than the best one.

TL;DR: It is shown that neural networks dominate time series approach form the point of yielding less mean absolute percentage error (MAPE) error and utilization of ANN instead of time series to obtain better predictions for energy consumption.

TL;DR: This paper proposes and compares different one-dimensional maps as chaotic search patterns in the constraint nonlinear optimization problems and applies them in specific optimization algorithm (weighted gradient direction based chaos optimization algorithm) and compares them based on numerical simulation results.

TL;DR: The new tanh–coth approach provides abundant solitons and kink solutions in addition to the existing ones and the power of this manageable method is confirmed.

TL;DR: Several Hadamard-type inequalities for products of two convex and s-convex functions are proved and some new inequalities for differentiable functions based on concavity and s -conveXity are established.

TL;DR: The Hirota’s direct method combined with the simplified version of this method is used to determine the N-soliton solutions for the Kadomtsev–Petviashvili (KP) equation.

TL;DR: A recursive programming technique is presented which reduces an order of magnitude for computing the minimum cross entropy thresholding objective function and a particle swarm optimization (PSO) algorithm is proposed for searching the near-optimal MCET thresholds.

TL;DR: An efficient numerical method for solution of nonlinear evolution equations based on the Haar wavelets approach is proposed and tested in the case of Burgers and sine-Gordon equations, demonstrating that the accuracy of theHaar wavelet solutions is quite high even in the cases of a small number of grid points.

TL;DR: The technique, NichePSO, extends the inherent unimodal nature of the standard PSO approach by growing multiple swarms from an initial particle population, each representing a different solution or niche; optimized individually.

TL;DR: The extended tanh method is used to establish abundant solitary wave solutions of nonlinear wave equations that include solitons, kinks and plane periodic solutions.

TL;DR: An epidemic transmission model SEIRS of malicious objects in the computer network is formulated, with death rate other than attack of malicious object is constant and an excess death rate constant for infective nodes.

TL;DR: An algorithm has been developed to convert the multi-order fractional differential equation into a system of fractionaldifferential equations and the Adomian decomposition method has been employed to solve the system of fractions.