A note on the modified simple equation method applied to Sharma-Tasso-Olver equation

Jawad et al. have applied the modified simple equation method to find the exact solutions of the nonlinear Fitzhugh-Naguma equation and the nonlinear Sharma-Tasso-Olver equation. The analysis of the Sharma-Tasso-Olver equation obtained by Jawad et al. is based on variant of the modified simple equation method. In this paper, we provide its direct application and obtain new 1- soliton solutions.     

A trust-region method applied to parameter identification of a simple prey–predator model

In this paper, the calibration of the non linear Lotka–Volterra model is used to compare the robustness and efficiency (CPU time) of different optimisation algorithms.Five versions of a quasi-Newton trust-region algorithm are developed and compared with a widely used quasi-Newton method. The trust-region algorithms is more robust and three of them are numerically cheaper than the more usual line search approach.Computation of the first derivatives of the objective function is cheaper with the backward differentiation (or adjoint model) technique than with the forward method as soon as the number of parameter is greater than a few ones. In the optimisation problem, the additional information about the Jacobian matrix made available by the forward method reduces the number of iterations but does not compensate for the increased numerical costs.A quasi-Newton trust-region algorithm with backward differentiation and BFGS update after both successful and unsuccessful iterations represents a robust and efficient algorithm that can be used to calibrate very demanding dynamic models.     

Numerical study of modified Adomian's method applied to Burgers equation

The application of Adomian's decomposition method to partial differential equations, when the exact solution is not reached, demands the use of truncated series. But the solution's series may have small convergence radius and the truncated series may be inaccurate in many regions. In order to enlarge the convergence domain of the truncated series, Padé approximants (PAs) to the Adomian's series solution have been tested and applied to partial and ordinary differential equations, with good results. In this paper, PAs, both in x$x$ and t$t$ directions, applied to the truncated series solution given by Adomian's decomposition technique for Burgers equation, are tested. Numerical and graphical illustrations show that this technique can improve the accuracy and enlarge the domain of convergence of the solution. It is also shown in this paper, that the application of Adomian's method to the ordinary differential equations set arising from the discretization of the spatial derivatives by finite differences, the so-called method of lines, may reduce the convergence domain of the solution's series.     

When should you sack a football manager? Results from a simple model applied to the English Premiership

What strategy should a football (soccer, in American parlance) club adopt when deciding whether to sack its manager? This paper introduces a simple model assuming that a club's objective is to maximize the number of league points that it scores per season. The club's strategy consists of three choices: the length of the honeymoon period during which it will not consider sacking a new manager, the level of the performance trapdoor below which the manager get the sack, and the weight that it will give to more recent games compared to earlier ones. Some data from the last six seasons of the English Premiership are used to calibrate the model. At this early stage of the research, the best strategy appears to have only a short honeymoon period of eight games (much less than the actual shortest period of 12 games), to set the trapdoor at 0.74 points per game, and to put 47% of the weight on the last five games. A club adopting this strategy would obtain on average 56.8 points per season, compared to a Premiership average of 51.8 points.     

A simple method for computing velocities from tracer observations and a model output

A method is suggested for estimating velocities by combining observations of a continuously distributed tracer and a circulation model output (background velocity field). A theoretical error analysis is provided and checked by simulations. The estimate reduces the model error by about 12–32% and the estimation procedure turns out to be of high computational efficiency. In addition, a compatibility measure between data and model is introduced which is also tested by simulations.     

A perturbation method applied to the buckling of a compressed elastica

We consider the problem of carrying out an asymptotic analysis for the phenomenon of bifurcation which occurs at critical values of an axial force applied to an elastic column. In the present setting a discontinuous coefficient precludes the possibility of carrying out the usual asymptotic analysis. The problem is overcome via a nonlinear change of independent variables.     

A self-adaptive trust region method with line search based on a simple subproblem model

In this paper, based on a simple model of the trust region subproblem, we propose a new self-adaptive trust region method with a line search technique for solving unconstrained optimization problems. By use of the simple subproblem model, the new method needs less memory capacitance and computational complexity. And the trust region radius is adjusted with a new self-adaptive adjustment strategy which makes full use of the information at the current point. When the trial step results in an increase in the objective function, the method does not resolve the subproblem, but it performs a line search technique from the failed point. Convergence properties of the method are proved under certain conditions. Numerical experiments show that the new method is effective and attractive for large-scale optimization problems.     

A modified adaptive-order rational Arnoldi method for model order reduction

A Greedy-type expansion point selection for moment-matching methods in model order reduction mainly depends on the computation of a sequence of reduced order models. Typically, the adaptive-order rational Arnoldi (AORA) method resembles an efficient way for the computation of a Galerkin projection corresponding to a set of expansion points. We will provide an extension of the AORA method, in order to reuse the orthonormal basis from previous calls of the AORA method. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A molecular method applied to a non-local PDE in stratified Lie groups

In this article we study a transport-diffusion equation in the framework of the stratified Lie groups. For this equation we will study the existence of the solutions, a maximum principle, a positivity principle and Hölder regularity.     

A variational method applied to a linear hyperbolic initial boundary value problem

This paper deals with the application of a variational method to a boundary value problem of the wave equation. Starting with an initial boundary value problem (which is given) introduction of a boundary condition at the final time leads to a boundary value problem with one of the initial conditions redundant. This redundant initial condition is used by the trial function of the direct method (of the Ritz type) which is employed to stationarize the variational principle.     

An averaging method applied to a duffing equation

We approximate a Duffing equation by an averaged system. We solve the system explicitely and draw bifurcation diagrams in dependence of the forcing term. We discuss the goodness of the averaging method, relative to the behavior of the solutions in dependence of involved parameters, by comparing with results obtained in [6,10] for the original Duffing equation.     

A simple time-delayed method to control chaotic systems

Based on the adaptive iterative learning strategy, a simple time-delayed controller is proposed to stabilize unstable periodic orbits (UPOs) embedded in chaotic attractors. This controller includes two parts: one is a linear feedback part; the other is an adaptive iterative learning estimation part. Theoretical analysis and numerical simulation show the effectiveness of this controller.     

A simple method to compute economic order quantities

In this note, a simple method by using the arithmetic–geometric-mean-inequality theorem is proposed to computer the global minimum economic order quantities without taking complex differential calculus or using tedious algebraic manipulations. In contrast to (Minner, S., 2007. A note on how to compute economic order quantity without derivatives by cost comparisons. International Journal of Production Economics 105, 293–296; Wee, H.M., Wang, W.T., Chung, C.J., 2009. A modified method to computer economic order quantities without derivatives by cost-difference comparisons. European Journal of Operational Research) based on a local cost minimum initially to derive the solution and then proven it’s the global minimum, the proposed method yields the global minimum cost immediately and explicitly without using the cost comparisons and letting the time horizon to infinity.     

A Cosmo-simula program for a simple air-pollution model

With a programmed example, the article introduces Cosmo-Simula, a language designed for the programming of continuous simulation. The language uses the Algol part of Simula for the programming of the algorithmic part and an extension of Cosmo for the programming of the administrative part of the problem. The translator is programmed using the Algol part of Simula and makes the extended Cosmo available for computers with an Algol-compiler.     

On a simple maximum principle technique applied to equations on the circle

For a class of general quasilinear equations on S¹, we show that, by a very simple maximum principle technique, as long as the solution stays finite, all of its derivatives also remain finite. Some specific examples are given. Under suitable assumptions, we also derive exponential decay of the derivatives of the solution.     

A directed topic model applied to call center improvement

We propose subject matter expert refined topic (SMERT) allocation, a generative probabilistic model applicable to clustering freestyle text. SMERT models are three‐level hierarchical Bayesian models in which each item is modeled as a finite mixture over a set of topics. In addition to discrete data inputs, we introduce binomial inputs. These ‘high‐level’ data inputs permit the ‘boosting’ or affirming of terms in the topic definitions and the ‘zapping’ of other terms. We also present a collapsed Gibbs sampler for efficient estimation. The methods are illustrated using real world data from a call center. Also, we compare SMERT with three alternative approaches and two criteria. Copyright © 2015 John Wiley & Sons, Ltd.     

A probabilistic model applied to emergency service vehicle location

This paper is concerned with the formulation and the solution of a probabilistic model for determining the optimal location of facilities in congested emergency systems. The inherent uncertainty which characterizes the decision process is handled by a new stochastic programming paradigm which embeds the probabilistic constraints within the traditional two-stage framework. The resulting model drops simplifying assumptions on servers independence allowing at the same time to handle the spatial dependence of demand calls. An exact solution method and different tailored heuristics are presented to efficiently solve the problem. Computational experience is reported with application to various networks.