Integrals For Systems Of Differential Equations Research Articles

Local improvements in numerical forecasts of relative humidity using polynomial solutions of general differential equations

Large‐scale forecast models are based on the numerical integration of differential equation systems, which can describe atmospheric processes in light of global meteorological observations. Mesoscale forecast systems need to define the initial and lateral boundary conditions, which may be carried out with robust global numerical models. Their overall solutions are able to describe the dynamic weather system on the Earth scale using a large number of complete globe 3D matrix variables in several atmospheric layers. Post‐processing methods using local measurements were developed in order to clarify surface weather details and adapt numerical weather prediction model outputs for local conditions. Differential polynomial network is a new type of neural network that can model local weather using spatial data observations to process forecasts of the input variables and revise the target 24 h prognosis. It defines and solves general partial differential equations, being able to describe unknown dynamic systems. The proposed forecast correction method uses a differential network to estimate the optimal numbers of training days and form derivative prediction models. It can improve final numerical forecasts, processed with additional data analysis and statistical techniques, in the majority of cases. The two‐stage procedure presented is analogous to the perfect‐prognosis method using real observations to derive a model, which is applied to the forecasts of the predictors to calculate output predictions.

Wind speed forecast correction models using polynomial neural networks

Accurate short-term wind speed forecasting is important for the planning of a renewable energy power generation and utilization, especially in grid systems. In meteorology it is usual to improve the forecasts by means of some post-processing methods using local measurements and weather prediction model outputs. Neural networks, trained with local real data observations can improve short-term wind speed forecasts with respect to meso-scale numerical meteorological model outcomes of the same data types in the majority of cases. Large-scale forecast models are based on the numerical integration of differential equation systems, which can describe atmospheric circulation processes on account of global meteorological observations. Several layer 3D complex models, which involve a large number of matrix variables, cannot exactly describe conditions near the ground, highly influenced by a landscape relief, coast, structure and other factors. Polynomial neural networks can form and solve general differential equations, which allow to model real complex systems by means of substitution derivative term sum series. The proposed adaptive method forms a correction function according to real observations and consequently applies forecasts to revise a desired prognosis in a selected locality.

Study of the Characteristics and Computation Analysis Results of Electromechanical Systems Models

Today, simulation of electrical drives with asynchronous motors based on systems of differential equations is regarded as one of the principal means of their research study. The difficulty of the simulation is determined by the need for accuracy of the results obtained and the complexity of the mathematical model's differential equations. In this article, we present a study of the particularities of the simulation of electrical drives systems with asynchronous motors. We have studied models composed of three-phase and orthogonal coordinates systems and we have shown that qualitative and quantitative differences exist in the process of changing the angular speed of the rotor and electromagnetic torque. The result obtained is above all influenced by the non-linear character of the load opposing a fan-type or dry friction-type resistant torque. For dual-earthed electromagnetic actuation with the moments of the resistant torques indicated, integration of differential equation systems was carried out with various digital methods used in professional mathematical software for simulation.

Détermination directe des constantes cinétiques d'une réaction chimique par microcalorimétrie à conduction application à la saponification des diesters

The kinetic study of competitive consecutive reactions presents difficulties owing to the complexity of the mathematical integration of differential equation systems. Many investigators adopted methods using graphs of experimental data to determine the kinetic constants of a reaction. We propose, in this work, a direct determination of these constants based on thermograms recorded with a Calvet conduction microcalorimeter using a computing program which includes numerical integration of differential equation systems, signal convolution with an experimental function of apparatus (to get rid of the inertness of the detector—recorder system) and the optimization of the adopted model parameters. We applied this exploitation process to the alkaline hydrolysis of some diester of diols or dicarboxylic acids in aqueous solution.