Forest fire modelling using cellular automata: application to the watershed Oued Laou (Morocco)

ABSTRACT

In this work, we consider the problem of modelling the phenomenon of forest fires using the cellular automata approach. The proposed model takes into account the main parameters that affect this phenomenon like nature and density of vegetation, humidity, wind, and altitude. We developed a decision-aided tool with JAVA which allows to analyse and format several hybrid collected data (satellite images, Digital Terrain Model) relatively to each studied area. The generated scenarios of forest fire spread in the study area will be considered as a guide for strategies in control and prevention of forest fires. As an application, we consider the watershed Oued Laou (Morocco).     

An optimal homotopy analysis method based on particle swarm optimization: application to fractional-order differential equation

This paper describes a new problem-solving mentality of finding optimal parameters in optimal homotopy analysis method (optimal HAM). We use particle swarm optimization (PSO) to minimize the exact square residual error in optimal HAM. All optimal convergence-control parameters can be found concurrently. This method can deal with optimal HAM which has finite convergence-control parameters. Two nonlinear fractional-order differential equations are given to illustrate the proposed algorithm. The comparison reveals that optimal HAM combined with PSO is effective and reliable. Meanwhile, we give a sufficient condition for convergence of the optimal HAM for solving fractional-order equation, and try to put forward a new calculation method for the residual error.     

On the qualitative behaviour of the solution to a stochastic partial functional - differential equation arising in population dynamics

Stability of the solution of a stochastic partial functional - differential equation that describes the evolution of a population is shown. A comparison between solutions of time-delayed problems and solutions of problems without time delay is given     

QML-Morven: A novel framework for learning qualitative differential equation models using both symbolic and evolutionary approaches

In this paper, a novel qualitative differential equation model learning (QML) framework named QML-Morven is presented. QML-Morven employs both symbolic and evolutionary approaches as its learning strategies to deal with models of different complexity. Based on this framework, a series of experiments were designed and carried out to: (1) investigate factors that influence the learning precision and minimum data requirement for successful learning; (2) address the scalability issue of QML systems.     

On the worst scenario method: A modified convergence theorem and its application to an uncertain differential equation

We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient. This research was supported in part by the project MSM4781305904 from the Ministry of Education, Youth and Sports of the Czech Republic.     

New approach to the Lax‐Wendroff modified differential equation for linear and nonlinear advection

The paper presents an enhanced analysis of the Lax‐Wendroff difference scheme—up to the eighth‐order with respect to time and space derivatives—of the modified‐partial differential equation (MDE) of the constant‐wind‐speed advection equation. The modified equation has been so far derived mainly as a fourth‐order equation. The Π ‐form of the first differential approximation (differential approximation or equivalent equation) derived by expressing the time derivatives in terms of the space derivatives is used for presenting the MDE. The obtained coefficients at higher order derivatives are analyzed for indications of the character of the dissipative and dispersive errors. The authors included a part of the stencil applied for determining the modified differential equation up to the eighth‐order of the analyzed modified differential equation for the second‐order Lax‐Wendroff scheme. Neither the derived coefficients at the space derivatives of order p ∈ (7 – 8) in the modified differential equation for the Lax‐Wendroff difference scheme nor the results of analyses on the basis of these coefficients of the group velocity, phase shift errors, or dispersive and dissipative features of the scheme have been published. The MDEs for 2 two‐step variants of the Lax‐Wendroff type difference schemes and the MacCormack predictor–corrector scheme (see MacCormack's study) constructed for the scalar hyperbolic conservation laws are also presented in this paper. The analysis of the inviscid Burgers equation solution with the initial condition in a form of a shock wave has been discussed on their basis. The inviscid Burgers equation with the source is also presented. The theory of MDE started to develop after the paper of C. W. Hirt was published in 1968.     

One-dimensional Schrödinger operator on the half-line: The differential equation for eigenfunctions with respect to the spectral parameter and an analog of the Freud equation

It is shown that the eigenfunctions of the Schrödinger operator on the half-line satisfy an explicitly constructed differential equation with respect to the spectral parameter. Such an equation was earlier obtained for orthogonal polynomials. An analog of the Freud equation is found.