Numerical Spline Method for Simulation of Stochastic Differential Equations systems: طريقة شرائحية عددية لمحاكاة حل نظم من المعادلات التفاضلية العشوائية

In this paper, numerical spline method is presented with collocation two parameters for solving systems of multi-dimensional stochastic differential equations (SDEs). Multi-Wiener's time-continuous process is simulated as a discrete process, and then the mean-square stability of proposed method when applied to a system of two-dimensional linear SDEs is studied. The study shows that the method is mean-square stability and third-order convergent when applied to a system of linear and nonlinear SDEs. Moreover, the effectiveness of our method was tested by solving two test linear and non-linear problems. The numerical results show that the accuracy and applicability of the proposed method are worthy of attention.

Dynamics of notified cases of dengue in Alagoas: Geospatialization and Applied Statistics

The aim of the study was to evaluate the reported cases of dengue in the State of Alagoas via applied statistics and geospatialization.Dengue data were obtained from the DATASUS system between 2000 and 2015. The time series was submitted to descriptive and exploratory statistics and the Pettitt test. In the dengue case maps, the Spline method via QGis version 3.4 was used. In descriptive statistics, only 10 municipalities were evaluated based on the largest case records. All municipalities were above the average of dengue cases in 2010, the year of the biggest recent flood in the state. The boxplot pointed out that all 10 municipalities were positive asymmetric in a few months for dengue cases, the exception was Delmiro Gouveia. The Pettitt test identified biannual cycles (2006/2007 and 2009/2010) associated with the phases of ENSO (El Niño and La Niña) in the moderate category, followed by the months of January, February, April and December, corresponding to the performance of some systems synoptics. In the mapping of annual cases of dengue, the highest records occurred in the Agreste and East Alagoas. Geospatialization and applied statistics are efficient in the spatiotemporal evaluation of dengue cases in Alagoas.

Error compensation based on surface reconstruction for industrial robot on two-dimensional manifold

Purpose This paper aims to present error compensation based on surface reconstruction to improve the positioning accuracy of industrial robots. Design/methodology/approach In previous research, it has been proved that the positioning error of industrial robots is continuous on the two-dimensional manifold of six-joint space. The point cloud generated by positioning error data can be used to fit the continuous surfaces, which makes it possible to apply surface reconstruction on error compensation. The moving least-squares interpolation and the B-spline method are used for the error surface reconstruction. Findings The results of experiments and simulations validate the effectiveness of error compensation by the moving least-squares interpolation and the B-spline method. Practical implications The proposed methods can control the average of compensated positioning error within 0.2 mm, which meets the requirement of a tolerance (±0.5 mm) for fastener hole drilling in aircraft assembly. Originality/value The error surface reconstruction based on the B-spline method has great superiority because fewer sample points are needed to use this method than others while keeping the compensation accuracy at the same level. The control points of the B-spline error surface can be adjusted with measured data, which can be applied for the error prediction in any temperature field.

Non-polynomial Cubic Spline Method for the Solution of Second-order Linear Hyperbolic Equation

Second-order linear hyperbolic equations are solved by using a new three level method based on nonpolynomial spline in the space direction and Taylor expansion in the time direction. Numerical results reveal that three level method based on non-polynomial spline is implemented and effective

Numerical solution of Hermite differential equation using the spline method of order 1 with GeoGebra

In this paper we will show the visualization of the approximations that can be obtained by means of the order 1 spline method for Hermite differential equations with well-interactive examples of GeoGebra applets. Here, we will dedicate ourselves to publisize, the great benefit that can be obtained, in the process of generating new mathematical knowledge for learning and teaching the numerical solutions of differential equations.